Question

what is the area of triangle qrs? 9 square units 7 square units 13 square units 10 square units

Explanation:

Step1: Identify coordinates of Q, R, S

Assume Q(2,-1), R(-4,1), S(-2,-3) from graph.

Step2: Apply shoelace formula

Area = $\frac{1}{2}|x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)|$

Step3: Substitute coordinates

$\frac{1}{2}|2(1-(-3)) + (-4)(-3-(-1)) + (-2)(-1-1)|$

Step4: Calculate inside absolute value

$2(4) + (-4)(-2) + (-2)(-2) = 8 + 8 + 4 = 20$

Step5: Compute area

$\frac{1}{2}|20| = 10$

Answer:

10 square units