Question

Points J (5,2) and K (-2,-5) are two vertices of a isosceles triangle. If L is the third vertex and has a y-coordinate of 4, what is the x-coordinate of L?

Answer 1

well there seem to be 2 options for this question

1. the sides LJ = KL

so make the vertex L =(x, 4)

and use the distance formula

the 2nd choice would be JK is one of the equal sides...

I think the 1st option is the easier

Answer 2

how do i do that

Answer 3

@campbell_st

Answer 4

ok... so let L be the point (x, 4)

so use the distance formula LJ

\[d_{LJ} = \sqrt{(x - 5)^2 +(4 - 2)^2}\]

and LK

\[d_{LK} = \sqrt{(x + 2)^2 +(4 + 5)^2}\]

equate the distances... since the triangle is isosceles

and sqaure both sides and you get

\[(x -5)^2 +(4 -2)^2 = (x +2)^2 + (4+5)^2\]

so now you can distribute, simplify then solve for x

hope it makes sense

Answer 5

hey can we use the pythagoream theorum instead because we don't use the distance formula

Answer 6

??

Answer 7

the distance formula is pythagoras. theorem

Answer 8

now looking at pythagoras

you can find LJ and LK in terms of pythagoras

then solve for x

that's all I did above.