Question

Is triangle ABC with vertices A(-1,4), B(3,1), and C(0,-3) a right triangle? Explain
your answer using the slopes of the segments that form the sides of the triangle.

Answer 1

Umm, did you try to graph it?

Answer 2

that's what I was thinking too

Answer 3

I mean do you have to graph it

Answer 4

You can find the slope between any two points by using: \[
\frac{y_2-y_1}{x_2-x_1}=m
\]

Answer 5

You know that two slopes are perpendicular if \(m_1m_2=-1\).

Answer 6

It's not a right triangle, I did graph it

Answer 7

But I don't think graphing it was required

Answer 8

but wouldn't you have to graph it to find out if it was a right triangle or not

Answer 9

Can you find slope for the AB segment using the formula I wrote?

Answer 10

I don't get slopes at all qq

Answer 11

The slope is the difference of the y coordinates divided by the difference of the x coordinates

Answer 12

^

Answer 13

So, for AB, we have \[
\frac{A_y-B_y}{A_x-B_x} = \frac{4-1}{-1-3}
\]

Answer 14

Ohh, so it's -1+3+0?

Answer 15

is that what you got

Answer 16

\[\frac{ 3 }{ -4 }\]

Answer 17

Okay, now can you find slope for AC and BC?

Answer 18

1,7 and 3,4 @wio

Answer 19

slope should be a fraction or whole number

Answer 20

Anyway, you have to multiply each two slopes, and if any of them multiply to \(-1\), then that means they're perpendicular.

Answer 21

I'm so lost;;;;

Answer 22

So, for AC, we have \[
\frac{A_y-C_y}{A_x-C_x} = \frac{4-(-3)}{-1-0}
\]