In △abc, the coordinates of vertices a and b are a(1,−1) and b(3,2). for each of the given coordinates of vertex c, is △abc a right triangle? select right triangle or not a right triangle for each set of coordinates. c(0,2) c(3,−1) c(0,4)

we know that

the formula to calculate the distance between two points is equal to

In this problem we have

Step 1

Find the distance AB

Substitute the values in the formula

Step 2

Find the distance AC1

Substitute the values in the formula

Step 3

Find the distance BC1

Substitute the values in the formula

Step 4

Find the distance AC2

Substitute the values in the formula

Step 5

Find the distance BC2

Substitute the values in the formula

Step 6

Find the distance AC3

Substitute the values in the formula

Step 7

Find the distance BC3

Substitute the values in the formula

we know that

If the length sides of the triangle satisfy the Pythagoras Theorem. then the triangle is a right triangle

The formula of the Pythagoras Theorem is equal to

where

c is the hypotenuse (the greater side)

a and b are the legs of the triangle

Step 8

Verify if the triangle ABC1 is a right triangle

we have

Applying Pythagoras theorem

--------> is not true

therefore

the triangle ABC1 is not a right triangle

Step 9

Verify if the triangle ABC2 is a right triangle

we have

Applying Pythagoras theorem

--------> is true

therefore

the triangle ABC2 is a right triangle

Step 10

Verify if the triangle ABC3 is a right triangle

we have

Applying Pythagoras theorem

--------> is true

therefore

the triangle ABC3 is a right triangle

therefore

the answer is