Question

Do these three points make a right triangle? A = (-3,-4), B= (-2,-2), C= (0, -3) Type your answers as a simplified radical. What is the distance between point A,(-3,-4) and point B (-2,-2)? What is the distance between point A,( -3, -4) and point C (0, -3)? What is the distance between point C,(0, -3) and point B (-2,-2)? Now use the Pythagorean Theorem. Do the squares of the the two short sides add to the square of the longer side? Distance from A to B squared is Distance from A to C squared is Distance from C to B squared is Do the three points form a right triangle?

Answer 1

We have the following points:

A = (-3,-4), B= (-2,-2), C= (0, -3)

What is the distance between point A,(-3,-4) and point B (-2,-2)?

`d=\sqrt[]{(-2+3)^2+(-2+4)^2}=\sqrt[]{5}`

What is the distance between point A,( -3, -4) and point C (0, -3)?

`d=\sqrt[]{(0+3)^2+(-3+4)^2}=\sqrt[]{10}`

What is the distance between point C,(0, -3) and point B (-2,-2)?

`d=\sqrt[]{(-2-0)^2+(-2+3)^2}=\sqrt[]{5}`

Do the squares of the the two short sides add to the square of the longer side?

Yes

Distance from A to B squared is

5

Distance from A to C squared is

10

Distance from C to B squared is

5

Do the three points form a right triangle?

Yes

Since:

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