Answer:
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.
