Question

which point on x-axis is equivalent from points 5,9 and -4,6?

Answer 1

Let the unknown point be $(x,0)$.

Then expression about the distance can be made.

Let distance $d$.

By the formula of distance,

$d^2=(x-5)^2+9^2=(x+4)^2+6^2$.

$(x-5)^2+9^2=(x+4)^2+6^2$

$x^2-10x+25+81=x^2+8x+16+36$

$-10x+106=8x+52$

$16x=54$

∴ $x=3$

Hence, the point is $(3,0)$!!!

Thank you!

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