Question

question 1(multiple choice worth 1 points) (04.01 mc) lydia graphed △def at the coordinates d (-2, -1), e (-2, 2), and f (0, 0). she thinks △def is a right triangle. is lydias assertion correct? yes; the slopes of (overline{ef}) and (overline{df}) are opposite reciprocals. yes; the slopes of (overline{ef}) and (overline{df}) are the same. no; the slopes of (overline{ef}) and (overline{df}) are not opposite reciprocals. no; the slopes of (overline{ef}) and (overline{df}) are not the same.

Explanation:

Step1: Recall slope - formula

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

Step2: Calculate the slope of $\overline{EF}$

For points $E(-2,2)$ and $F(0,0)$, $m_{EF}=\frac{0 - 2}{0+2}=\frac{-2}{2}=-1$.

Step3: Calculate the slope of $\overline{DF}$

For points $D(-2,-1)$ and $F(0,0)$, $m_{DF}=\frac{0 + 1}{0+2}=\frac{1}{2}$.

Step4: Check the relationship between slopes

The slopes $m_{EF}=-1$ and $m_{DF}=\frac{1}{2}$ are not opposite - reciprocals.

Answer:

C. No; the slopes of $\overline{EF}$ and $\overline{DF}$ are not opposite reciprocals.