Question

Can I get some help with this question?

Answer 1

We see the vertex (-3,2) makes a vertical line with (-3,-3) and a horizontal line with (1,2) so the right angle is at (-3,2) and the hypotenuse is the segment between (-3,-3) and (1,2).

The distance formula tells us

$d = \sqrt{(-3 -1)^2 + (-3 - 2)^2} =\sqrt{4^2+5^2}= \sqrt{41}$

Now we go through the choices.

The length of the hypotenuse is $\sqrt{41}$. That's CORRECT

Use the Pythagorean Theorem. That's CORRECT, the distance formula is just the Pythagorean Theorem on the Cartesian grid.

The hyp is $\sqrt{20}$. That's incorrect.

Find the slope. That's incorrect; it doesn't help calculate the length.

Use the distance formula. That's what we did. CORRECT.

The length of the hyp is 3. That's incorrect.

Use the midpoint formula. That's no help for the distance; incorrect.

Not possible; It's possible, we did it, this is incorrect.