Questions: U(1,1), V(-2,3), W(-8,-3), and X(-5,-5) form quadrilateral

Transcript text: $U(1,1), V(-2,3), W(-8,-3)$, and $X(-5,-5)$ form quadrilateral

Solution

Solution Steps

Step 1: Find the slope of UV

The slope of the line segment UV with points $U(1, 1)$ and $V(-2, 3)$ is given by $m_{UV} = \frac{3 - 1}{-2 - 1} = \frac{2}{-3} = -\frac{2}{3}$.

Step 2: Find the slope of WX

The slope of the line segment WX with points $W(-8, -3)$ and $X(-5, -5)$ is given by $m_{WX} = \frac{-5 - (-3)}{-5 - (-8)} = \frac{-5 + 3}{-5 + 8} = \frac{-2}{3} = -\frac{2}{3}$.

Step 3: Find the slope of UW

The slope of the line segment UW with points $U(1, 1)$ and $W(-8, -3)$ is given by $m_{UW} = \frac{-3 - 1}{-8 - 1} = \frac{-4}{-9} = \frac{4}{9}$.

Step 4: Find the slope of VX

The slope of the line segment VX with points $V(-2, 3)$ and $X(-5, -5)$ is given by $m_{VX} = \frac{-5 - 3}{-5 - (-2)} = \frac{-8}{-5 + 2} = \frac{-8}{-3} = \frac{8}{3}$.

Final Answer:

Since $m_{UV} = m_{WX} = -\frac{2}{3}$, the line segments UV and WX are parallel. Since $m_{UW} = \frac{4}{9}$ and $m_{VX} = \frac{8}{3}$, the line segments UW and VX are not parallel. The quadrilateral UVWX is a trapezoid because it has one pair of parallel sides (UV and WX).

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