Triangle QRS, with vertices Q(3,-6), R(7,-5) , and S(4,-2) , is drawn inside a rectangle, as shown below. What is the area, in square units, of triangle QRS?
To find the area of triangle QRS, we can use the formula for the area of a triangle given its vertices:
Area = 1/2 * |x1(y2-y3) + x2(y3-y1) + x3(y1-y2)|
Plugging in the coordinates of Q(3,-6), R(7,-5), and S(4,-2), we get:
Area = 1/2 * |3(-5 -(-2)) + 7(-2 -(-6)) + 4(-6 -(-5))|
Area = 1/2 * |3(-3) + 7(4) + 4(-1)|
Area = 1/2 * |-9 + 28 - 4|
Area = 1/2 * 15
Area = 7.5 square units
Therefore, the area of triangle QRS is 7.5 square units.