Answer:
The sum of the slopes of the three sides of the triangle is 3/2.
Step-by-step explanation:
Given information: The vertices of triangle are R(0,0), S(7,0), and T(2,5).
We need to find the sum of the slopes of the three sides of the triangle.
Slope formula:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
Using slope formula, the slope of segment RS is
[tex]m_{RS}=\frac{0-0}{7-0}=0[/tex]
[tex]m_{RT}=\frac{5-0}{2-0}=\frac{5}{2}[/tex]
[tex]m_{ST}=\frac{5-0}{2-7}=\frac{5}{-5}=-1[/tex]
The sum of the slopes of the three sides of the triangle is
[tex]Sum=m_{RS}+m_{RT}+m_{ST}[/tex]
[tex]Sum=0+\frac{5}{2}+(-1)[/tex]
[tex]Sum=\frac{5-2}{2}[/tex]
[tex]Sum=\frac{3}{2}[/tex]
Therefore the sum of the slopes of the three sides of the triangle is 3/2.
