JEE Questions for Maths Rectangular Cartesian Coordinates Quiz 3 - MCQExams.com

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
  • (5, 4)
  • (5 + √2, 4 + √2)
  • (5 - √2, 4 - √2)
  • None of these
The triangle joining the points P(2,Q (4, -and R (- 2,is
  • isosceles triangle
  • equilateral triangle
  • right angled triangle
  • None of these
if the line 2x + 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
  • 29/5
  • 5
  • 6
  • 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
  • √2
  • (3/2)1/2
  • (1/2)1/2
  • (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,
Maths-Rectangular Cartesian Coordinates-46648.png
  • 0
  • 1
  • - 1
  • a2 + b2
The line x + y = 4 divides the line joining the points (-1,and (5,in the ratio
  • 2 : 1
  • 1 : 2 externally
  • 1 : 2 externally
  • None of these
The points A (1, 2), B (2,and C (4,form a/an
  • isosceles triangle
  • equilateral triangle
  • straight line
  • 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.
  • √65
  • √117
  • √85
  • √116
The three distinct A (at21, 2at1) , B(at22, 2at2) and C(0,a) (where, a is a real number) are collinear. If
  • t1t2 = - 1
  • t1t2 = 1
  • 2t1t2 = t1 + t2
  • 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
  • -6, 8
  • 6, 8
  • -8, 6
  • -7, 7
If the three points (0, 1), (0, -and (x,are vertices of an equilateral triangle, then the values of x are
  • √3, √2
  • √3, - √3
  • - √5, √3
  • √2, - √2
  • √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
  • (1/3, 2)
  • (2, 1/3)
  • (2, 7)
  • (7, 2)
The point on the line 3x + 4y = 5, which is equidistant from (1,and (3,is
  • (7, - 4)
  • (15, - 10)
  • (1/7, 8/7)
  • (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,
  • P lies on the line segment RQ
  • Q lies on the line segment PR
  • R lies on the line segment QP
  • 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
  • 2 + √2
  • 2 - √2
  • 1 + √2
  • 1 - √2
The equation of the circle circumscribing the triangle formed by the lines x + y = 6, 2x + y = 4 and x + 2y = 5 is
  • x2 + y2 + 17x + 19y - 50 = 0
  • x2 + y2 - 17x - 19y - 50 = 0
  • x2 + y2 + 17x - 19y - 50 = 0
  • x2 + y2 - 17x - 19y + 50 = 0
The circumcentre of the triangle formed by the lines y = x, y = 2x and y = 3x + 4 is
  • (6, 8)
  • (6, - 8)
  • (3, 4)
  • (-3, - 4)
Circumcentre of the triangle whose vertices are (0, 0), (3,and (0,is
  • (3/2, 2)
  • (2, 3/2)
  • (0, 0)
  • None of these
The circumcentre of a triangle formed by the lines xy + 2x + 2y + 4 = 0 and x + y + 2 = 0, is
  • (-1, -1)
  • (0, -1)
  • (1, 1)
  • (-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
  • (4/3, 3)
  • (3, 2/3)
  • (3, 4/3)
  • (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
  • (1, 7/3)
  • (1/3, 7/3)
  • (-(1/3), 7/3)
  • (-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 = 2x, then θ is equal to
  • tan-1 2
  • tan-1 3
  • tan-1 (-3)
  • 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
  • 6
  • 9
  • 69
  • 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
  • (1, 3)
  • (0, 2)
  • (-1, 3)
  • (-3, -2)
If the points (a, b) , (a', b') and (a - a', b - b') are collinear, then
  • ab' = a' b'
  • ab = a' b'
  • aa' = bb'
  • 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
  • 25 cm2
  • 30 cm2
  • 36 cm2
  • 24 cm2
  • 48 cm2
The area of the segment of a circle of radius a subtending an angle of 2α at the center is

  • Maths-Rectangular Cartesian Coordinates-46655.png
  • 2)
    Maths-Rectangular Cartesian Coordinates-46656.png

  • Maths-Rectangular Cartesian Coordinates-46657.png
  • a2α
The straight lines x + 3y - 4 = 0 form a triangle which is
  • right angled
  • equilateral
  • isosceles
  • None of these
A triangle with vertices (4, 0), (- 1, -and (3,is
  • isosceles and right angled
  • isosceles but not right angled
  • right angled but not isosceles
  • 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
  • x2 + 4xy - y2 = 0
  • 2x2 - 4xy + y2 = 0
  • x2 - 4xy + y2 = 0
  • x2 - 4xy - y2 = 0
0:0:1


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