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JEE Questions for Maths Rectangular Cartesian Coordinates Quiz 3 - MCQExams.com
JEE
Maths
Rectangular Cartesian Coordinates
Quiz 3
If a point P(4,is shifted by a distance -√2 unit parallel to the line y =
x
, then coordinates of P in new position are
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(5, 4)
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(5 + √2, 4 + √2)
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(5 - √2, 4 - √2)
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None of these
The triangle joining the points P(2,Q (4, -and R (- 2,is
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isosceles triangle
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equilateral triangle
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right angled triangle
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None of these
if the line 2
x
+ y = k passes through the point which divides the segment joining the points (1,and (2,in the ratio 3 : 2, then k is equal to
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29/5
0%
5
0%
6
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11/15
The equation of the base BC of an equilateral ∆ABC is
x
+ y = 2 and A is (2, - 1). The length of the side of the triangle is
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√2
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(3/2)1/2
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(1/2)1/2
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(2/3)1/2
The line joining A(b cos α, b sin α) and B ( a cos β, a sin β), where a ≠ b, is produced to the point M (
x
, y ), so that AM : MB = b : a. Then,
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0
0%
1
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- 1
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a2 + b2
The line
x
+ y = 4 divides the line joining the points (-1,and (5,in the ratio
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2 : 1
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1 : 2 externally
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1 : 2 externally
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None of these
The points A (1, 2), B (2,and C (4,form a/an
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isosceles triangle
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equilateral triangle
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straight line
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right angled triangle
The vertices of ∆ABC are A (2, 2), B(-4, -and C(5, -8). Find the length of a median of a triangle, which is passing through the point C.
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√65
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√117
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√85
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√116
The three distinct A (at
2
1
, 2at
1
) , B(at
2
2
, 2at
2
) and C(0,a) (where, a is a real number) are collinear. If
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t1t2 = - 1
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t1t2 = 1
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2t1t2 = t1 + t2
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t1 + t2 = a
If the distance between (2,and (-5,is equal to the distance between (
x
,and (1, 3), then the values of
x
are
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-6, 8
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6, 8
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-8, 6
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-7, 7
If the three points (0, 1), (0, -and (
x
,are vertices of an equilateral triangle, then the values of
x
are
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√3, √2
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√3, - √3
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- √5, √3
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√2, - √2
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√5, - √5
If C is a point on the line segment joining A (-3,and B(2,such that AC = 2 BC, then the coordinate of C is
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(1/3, 2)
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(2, 1/3)
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(2, 7)
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(7, 2)
The point on the line 3
x
+ 4y = 5, which is equidistant from (1,and (3,is
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(7, - 4)
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(15, - 10)
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(1/7, 8/7)
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(0, 5/6)
Consider, three points P = [ - sin (β - α), - cos β], Q = [cos (β - α), sin β] and R = [cos (β - α + θ), sin (β - θ)] where 0 < α, β , θ < π/4. Then,
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P lies on the line segment RQ
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Q lies on the line segment PR
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R lies on the line segment QP
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P, Q and R are non - collinear
The
x
- co ordinate of the incentre of the triangle that has the coordinates of mid - points of its sides as (0,(1,and (1, 0 ) is
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2 + √2
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2 - √2
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1 + √2
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1 - √2
The equation of the circle circumscribing the triangle formed by the lines
x
+ y = 6, 2
x
+ y = 4 and
x
+ 2y = 5 is
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x2 + y2 + 17x + 19y - 50 = 0
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x2 + y2 - 17x - 19y - 50 = 0
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x2 + y2 + 17x - 19y - 50 = 0
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x2 + y2 - 17x - 19y + 50 = 0
The circumcentre of the triangle formed by the lines y =
x
, y = 2
x
and y = 3
x
+ 4 is
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(6, 8)
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(6, - 8)
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(3, 4)
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(-3, - 4)
Circumcentre of the triangle whose vertices are (0, 0), (3,and (0,is
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(3/2, 2)
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(2, 3/2)
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(0, 0)
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None of these
The circumcentre of a triangle formed by the lines
x
y + 2
x
+ 2y + 4 = 0 and
x
+ y + 2 = 0, is
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(-1, -1)
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(0, -1)
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(1, 1)
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(-1, 0)
If O( 0, 0 ), P( 3,4 ), Q( 6,0 ) be the vertices of the ∆OPQ.The point R inside ∆OPQ is such that the triangles OPR, PQR and OQR are of equal area. Then, the coordinates of R are
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(4/3, 3)
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(3, 2/3)
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(3, 4/3)
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(4/3, 2/3)
If a vertex of a triangle is (1,and the mid-points of two sides through the vertex are ( -1,and (3, 2), then the centroid of the triangle is
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(1, 7/3)
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(1/3, 7/3)
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(-(1/3), 7/3)
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(-1, 7/3)
If the centroid of the triangle formed by the points (0. 0), (cos θ, sin θ) and ( sin θ, - cos θ) lies on the line y = 2
x
, then θ is equal to
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tan-1 2
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tan-1 3
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tan-1 (-3)
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tan-1 (-2)
If A = (- 3, 4 ), B = (-1,- 2), C = (5,and D (
x
, - 4 ) are vertices of a quadrilateral such that ∆ABD = 2 ∆ACD.Then,
x
is equal to
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6
0%
9
0%
69
0%
96
Let A (1, k ), B (1,and C ( 2, 1 ) be the vertices of a right angled triangle with AC as its hypotenuse. If the area of the triangle is 1, then the set of values which \'k\' can take is given by
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(1, 3)
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(0, 2)
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(-1, 3)
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(-3, -2)
If the points (a, b) , (a', b') and (a - a', b - b') are collinear, then
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ab' = a' b'
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ab = a' b'
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aa' = bb'
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a2 + b2
ABC is a right angled triangle with ∠B = 90°, a = 6 cm. If the radius of the circumcircle is 5 cm. Then, the area of ∆ ABC is
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25 cm2
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30 cm2
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36 cm2
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24 cm2
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48 cm2
The area of the segment of a circle of radius a subtending an angle of 2α at the center is
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0%
2)
0%
0%
a2α
The straight lines
x
+ 3y - 4 = 0 form a triangle which is
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right angled
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equilateral
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isosceles
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None of these
A triangle with vertices (4, 0), (- 1, -and (3,is
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isosceles and right angled
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isosceles but not right angled
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right angled but not isosceles
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neither right angled nor isosceles
Locus of a point which moves such that its distance from the X-axis is twice its distance from the line
x
- y = 0 is
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x2 + 4xy - y2 = 0
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2x2 - 4xy + y2 = 0
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x2 - 4xy + y2 = 0
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x2 - 4xy - y2 = 0
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