Explanation
Distance between two points (x1,y1) and(x2,y2) can be calculated using theformula √(x2−x1)2+(y2−y1)2Distance between the points A(4,1) and B(3,a)=√10
=>√(3−4)2+(a−1)2=√10
√1+(a−1)2=√10
1+(a−1)2=10
(a−1)2=9
a−1=±3
=>a−1=3;a−1=−3
Let the point on the x-axis be (x,0) Distance between (x,0) and (7,6)=√(7−x)2+(6−0)2=√72+x2−14x+36=√x2−14x+85Distance between (x,0) and (−3,4)=√(−3−x)2+(4−0)2=√32+x2+6x+16=√x2+6x+25As the point (x,0) is equidistant from the two points, both the distancescalculated are equal. √x2−14x+85=√x2+6x+25=>x2−14x+85=x2+6x+2585−25=6x+14x60=20xx=3Thus, the point is (3,0)
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