Question

Triangle QRS, with vertices Q(3,3), R(9,2), and S(6,8), is drawn inside a rectangle, as shown below. What is the area in square units of triangle QRS

Answer 1

To find the area of triangle QRS, we can use the formula for the area of a triangle given its vertices in the coordinate plane:

Area = 1/2 * |x1(y2 - y3) + x2(y3 - y1) + x3(y1 - y2)|

Plugging in the coordinates of the vertices Q(3,3), R(9,2), and S(6,8), we get:

Area = 1/2 * |3(2 - 8) + 9(8 - 3) + 6(3 - 2)|
Area = 1/2 * |3(-6) + 9(5) + 6(1)|
Area = 1/2 * |-18 + 45 + 6|
Area = 1/2 * 33
Area = 16.5 square units

Therefore, the area of triangle QRS is 16.5 square units.