Question

which statement is true concerning the slope of the line formed by the hypotenuse of each triangle? a the slope formed by △cde has a value that is 1/2 the slope formed by △abc b the slope formed by △abc has a value that is 2 times greater than the slope formed by △cde c the slope formed by △cde has a value that is 2 times greater than the slope formed by △abc d the slope formed by △abc has a slope that is equal to the slope formed by △cde

Explanation:

Step1: Recall slope formula

The slope formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$.

Step2: Find slope of $\triangle ABC$

Let $A=(2,2)$, $B=(3,6)$. Then $m_{ABC}=\frac{6 - 2}{3 - 2}=\frac{4}{1}=4$.

Step3: Find slope of $\triangle CDE$

Let $C=(8,6)$, $D=(10,8)$. Then $m_{CDE}=\frac{8 - 6}{10 - 8}=\frac{2}{2}=1$. But if we consider the right - angled triangles on the line, the line is straight, and for any two points on a straight line, the slope is the same. In fact, if we use the overall points on the line, say for the big - picture line passing through all the relevant points, the slope between any two points on that line will be consistent. The two triangles are similar and lie on the same line. So the slope of the hypotenuse of $\triangle ABC$ and $\triangle CDE$ is equal.

Answer:

D. The slope formed by $\triangle ABC$ has a slope that is equal to the slope formed by $\triangle CDE$