Atriangle with vertices (3, −2), (7, 3), and (−7, 6) is what type of triangle?

equilateral
obtuse scalene
isosceles right
right

It's the last choice: Right angled.

Step-by-step explanation:

Evaluate the slopes of the lines joining the points:

Line joining (3,-2) and (7,3):

Slope = (3- -2) / (7-3) = 5/4.

Line joining (7,3 ) and (-7,6):

Slope = (6,3) / (-7-7) = -3/14.

Line joining (3,-2) and (-7,6):

Slope = (6- -2) / (-7 - 3) = -4/5

If we multiply the slope of this last line and the line joining (3,-2) and (7,3) we get 5/4 * -4/5 = -1 , so these 2 lines are perpendicular.

Therefore it is a right angled triangle.

It could also be isosceles so we check the length of the sides.

The length of the line joining (3, -2) and  (7.3)

=  √(3 - -2)^2 + (7-3)^2

= √41

The line joining (7,3) and (-7,6):

length is √(6-3)^2 + (-7-7)^2)

= √(205).

The line joining (3,-2) and (-7,6):

length is √(6- - 2)^2 + (-7-3)^2)

= √164

All sides have a different lengths so it is not isosceles.