Question

1. what is the slope of triangle xyz? what is the slope of vwx? what can you determine from the slopes?

Explanation:

Step1: Recall slope formula

The slope formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$, where $(x_1,y_1)$ and $(x_2,y_2)$ are two points on the line.

Step2: Identify points for triangle XYZ

For line segment XZ, assume $X=(x_1,y_1)$ and $Z=(x_2,y_2)$. From the graph, if $X=(1, - 1)$ and $Z=(5,-4)$. Then $m_{XZ}=\frac{-4-(-1)}{5 - 1}=\frac{-4 + 1}{4}=\frac{-3}{4}$. Since we are not given a clear - defined 'triangle XYZ' in terms of a non - degenerate triangle with three distinct non - collinear points for the slope of the whole triangle, if we assume we are talking about the slope of a side (here XZ), the slope is $-\frac{3}{4}$. For line segment VW, assume $V=(x_1,y_1)$ and $W=(x_2,y_2)$. If $V=(-4,2)$ and $W=(1,-1)$, then $m_{VW}=\frac{-1 - 2}{1-(-4)}=\frac{-3}{5}$.

Step3: Analyze what can be determined from slopes

If two lines have equal slopes, they are parallel. If the product of their slopes is - 1, they are perpendicular. Here, since $m_{VW}=-\frac{3}{5}$ and $m_{XZ}=-\frac{3}{4}$, the lines VW and XZ are neither parallel nor perpendicular.

Answer:

The slope of VW is $-\frac{3}{5}$, the slope of XZ (assuming we consider side XZ for 'triangle XYZ') is $-\frac{3}{4}$, and from the slopes we can determine that the lines VW and XZ are neither parallel nor perpendicular.