Question

10. The coordinates of a point on the X-axis which lie on the perpendicular

bisector of the line segment joining (7,6) and (-3,4) are​

Answer 1

Answer:

Step-by-step explanation:

Answer 2

Answer:

$(3,0)$

Step-by-step explanation:

Given: Line segment joining $(7,6)$ and $(-3,4)$ & a point on x-axis such that it also lies on perpendicular bisector of line.

To find: Coordinate of point.

Let the coordinate of point be $(x,y)$ .

$\begin{aligned}\sqrt{(x-7)^{2}+(y-6)^{2}} &=\sqrt{(x-(-3))^{2}+(y-4)^{2}} \\(x-7)^{2}+(y-6)^{2} &=(x+3) 62+(y-4)^{2} \\x^{2}-14 x+49+y^{2}-12 y+36 &=x^{2}+6 x+9+y^{2}-8 y+16 \\-14 x-6 x-12 y-8 y+49+36-9-16 &=0 \\-20 x+20 y+60 &=0 \\x-y-3 &=0 \\x-y=3\end{aligned}$

As the point lies on X-axis so put $y=0$ in $x-y=3$

$x=3$

Hence, coordinate is $(3,0).$

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