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mcouil9369

14.02.2021

Mathematics

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:

$m=\frac{y_2-y_1}{x_2-x_1}$

Using slope formula, the slope of segment RS is

$m_{RS}=\frac{0-0}{7-0}=0$

$m_{RT}=\frac{5-0}{2-0}=\frac{5}{2}$

$m_{ST}=\frac{5-0}{2-7}=\frac{5}{-5}=-1$

The sum of the slopes of the three sides of the triangle is

$Sum=m_{RS}+m_{RT}+m_{ST}$

$Sum=0+\frac{5}{2}+(-1)$

$Sum=\frac{5-2}{2}$

$Sum=\frac{3}{2}$

Therefore the sum of the slopes of the three sides of the triangle is 3/2.

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