Answer:
[tex]Area = 140[/tex]
Step-by-step explanation:
Given
R(6, 10)
Q(-9, 5)
S(2, -10)
Required
Area of triangle RQS
The are of RQS is calculated using the following formula;
[tex]Area = \frac{1}{2} [R_x(S_y - Q_y) + Q_x(R_y - S_y) + S_x(Q_y - R_y)][/tex]
Where x and y represent the axis of the given coordinates;
Given that R(6, 10);
[tex]R_x = 6 ; R_y = 10[/tex]
Given that Q(-9, 5);
[tex]Q_x = -9 ; Q_y = 5[/tex]
Given that S(2, -10);
[tex]S_x = 2 ; S_y = -10[/tex]
By Substituting these values in the given formula;
[tex]Area = \frac{1}{2} [R_x(S_y - Q_y) + Q_x(R_y - S_y) + S_x(Q_y - R_y)][/tex]
[tex]Area = \frac{1}{2} [6(-10 -5) + -9(10 - (-10)) + 2(5 - 10)][/tex]
[tex]Area = \frac{1}{2} [6(-15) + -9(10 + 10)) + 2(-5)][/tex]
[tex]Area = \frac{1}{2} [-90 + -9(20)) - 10][/tex]
[tex]Area = \frac{1}{2} [-90 -180 - 10][/tex]
[tex]Area = \frac{1}{2} [-280][/tex]
The expression |-280| means absolute value of -280 and the value is 280
[tex]Area = \frac{1}{2} [-280][/tex]
[tex]Area = \frac{1}{2}* 280[/tex]
[tex]Area = 140[/tex]
Hence, the area of the triangle is 140
