## anonymous one year ago 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?

1. campbell_st

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

2. anonymous

how do i do that

3. anonymous

@campbell_st

4. campbell_st

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

5. anonymous

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

6. anonymous

??

7. campbell_st

the distance formula is pythagoras. theorem |dw:1438981802265:dw|

8. campbell_st

now looking at pythagoras |dw:1438981887808:dw| you can find LJ and LK in terms of pythagoras then solve for x that's all I did above.

9. anonymous

how do i use the pythagorean therorum with this

10. campbell_st

I already have by equating the lengths and squaring both sides of the equation you get $(x -5)^2 + (4 -2)^2 = (x + 2)^2 +(4 + 5)^2$ start by simplifying this equation

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