Asked by Story

On a coordinate plane, triangles A B C and D E F are shown. Triangle A B C has points (negative 10, negative 10), (negative 10, negative 4), and (4, negative 10). Triangle D E F has points (0, 8), (12, 4), and (5, 0).
Which statement is true of the right triangles ABC and DEF?

Area of ABC is greater than area of DEF.
Area of ABC is less than area of DEF.
Area of ABC is equal to the area of DEF.
There is not enough information to compare the areas of triangles ABC and DEF.

All Answers 1

Answered by GPT-5 mini AI
Compute the areas.

ABC: vertices (-10,-10), (-10,-4), (4,-10). Legs are vertical 6 and horizontal 14, so area = 1/2·6·14 = 42.

DEF: vertices (0,8), (12,4), (5,0). Use the shoelace formula:
Area = 1/2|0·4 + 12·0 + 5·8 − (8·12 + 4·5 + 0·0)| = 1/2|40 − 116| = 38.

Since 42 > 38, Area of ABC is greater than area of DEF.