Question

The coordinates of the plotted points are labeled as left parenthesis negative 7 comma 3 right parenthesis, left parenthesis 5 comma 8 right parenthesis, and left parenthesis 0 comma negative 2 right parenthesis. The points are joined by solid lines to form a triangle.


Peeta draws a triangle on the coordinate grid. What is the area of their triangle in square units?

(1 point)
Responses

65
65

40.5
40.5

120
120

47.5

Answer 1

Use the shoelace formula. For vertices (-7,3), (5,8), (0,-2):

Sum1 = (-7)(8) + (5)(-2) + (0)(3) = -56 - 10 + 0 = -66
Sum2 = (3)(5) + (8)(0) + (-2)(-7) = 15 + 0 + 14 = 29
Area = 1/2 |Sum1 - Sum2| = 1/2 | -66 - 29 | = 1/2 (95) = 47.5

So the area is 47.5 square units.