SOLUTION: Find the point (𝑥,𝑦)
on the line 𝑦=𝑥
that is equidistant from the points (10,−10)
and (−4,6)
.
Algebra.Com
Question 1203786: Find the point (𝑥,𝑦)
on the line 𝑦=𝑥
that is equidistant from the points (10,−10)
and (−4,6)
.
Found 3 solutions by josgarithmetic, mananth, ikleyn:
Answer by josgarithmetic(39618) (Show Source): You can put this solution on YOUR website!
Because you want x=y or y=x
sq. both sides, and making substitution
.
.
.
The point, (-37,-37)
Answer by mananth(16946) (Show Source): You can put this solution on YOUR website!
Find the point (𝑥,𝑦)
on the line 𝑦=𝑥
that is equidistant from the pointsA (10,−10)
and B(−4,6)
The distance between two points (x₁, y₁) and (x₂, y₂) is given by:
Square both sides andplug the given values
(x+4)^2+(y-6)^2= (x-10)^2+(y+10)^2
expand
x^2+8x+16 +y^2-12y+36 = x^2-20x+100 +y^2+20y+100
8x+16-12y+36 = -20x +100+20y+100
combine like terms
28x-32y =148 but x=y
-4x = 148
x=37 ---> y=37
(37,37)
point (x, y) that is equidistant from the points (10, -10) and (-4, 6) is indeed (37, 37).
Answer by ikleyn(52797) (Show Source): You can put this solution on YOUR website!
.
The answer (37,37) by @mananth is INCORRECT.
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