Question

Here is the question and the multiple-choice options from Item 20 of the Geometry A Semester Exam on your screen.📐 Geometry A Semester Exam Question (Item 20)Question:Use the image to answer the question.The coordinates of the plotted points are labeled as $(-7, 3)$, $(5, 8)$, and $(0, -2)$. 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)Multiple Choice Options (Responses)( ) $40.5$( ) $65$( ) $47.5$( ) $120$

Answer 1

Use the shoelace formula. For points A(−7,3), B(5,8), C(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

Answer: 47.5.