Question

Indicate the equation of the given line in standard form.

The line containing the hypotenuse of right triangle ABC where A(-5, 5), B(1, 1), and C(3, 4) are the vertices.

I worked it out and got x+8y=31 but I'm not sure if its right...

Answer 1

you're close, but not quite there

Answer 2

The left side is correct (x+8y), but the right side is NOT correct (it should be some number that is not 31)

Answer 3

This is how i worked it out....

Answer 4

1. midpoint of AB = 1/2(1-5), 1/2(1+5)
=-2,3
2. midpoint of BC = 1/2(3+1), 1/2(4+1)
= 2,5/2

Answer 5

why are you looking for midpoints?

Answer 6

oh my bad. I put the wrong question lol. It's this:
Indicate the equation of the given line in standard form.

The line containing the midpoints of the legs of right triangle ABC where A(-5, 5), B(1, 1), and C(3, 4) are the vertices.

Answer 7

ok one sec

Answer 8

ok you have the correct midpoints

Answer 9

feel free to keep going

Answer 10

but do i still have it wrong??

Answer 11

yes

Answer 12

the left side of x+8y is correct, but the right side is not

Answer 13

for now, set the left side equal to some number C

x+8y = C

Now plug in one midpoint, say (-2, 3) to get

x+8y = C

-2+8(3) = C ... plug in x = -2 and y = 3

-2 + 24 = C

22 = C

C = 22

Answer 14

So this proves that (-2,3) is on the line x+8y = 22

Answer 15

you can check the other midpoint, but it should work out as well

Answer 16

so the line through those two midpoints is x+8y = 22

Answer 17

Thanks jimmy :)

Answer 18

you're welcome