Question

question 1-7
the quadrilateral wxyz is a square. the coordinates of the vertices w and x are (-3, 2) and (5, 3) respectively. click to match each side of the square with its slope.
(chart with columns: 1/8, -8 and rows: side zw, side xy, side yz, side xw with checkboxes)

Explanation:

Step1: Calculate slope of WX

The formula for slope between two points \((x_1,y_1)\) and \((x_2,y_2)\) is \(m = \frac{y_2 - y_1}{x_2 - x_1}\). For \(W(-3,2)\) and \(X(5,3)\), slope of \(WX\) is \(\frac{3 - 2}{5 - (-3)}=\frac{1}{8}\).

Step2: Determine slope of XY (perpendicular to WX)

If two lines are perpendicular, the product of their slopes is \(- 1\). Let slope of \(XY\) be \(m_{XY}\), then \(\frac{1}{8}\times m_{XY}=-1\), so \(m_{XY}=-8\).

Step3: Determine slope of YZ (parallel to WX)

Parallel lines have equal slopes, so slope of \(YZ\) is equal to slope of \(WX\), which is \(\frac{1}{8}\).

Step4: Determine slope of ZW (parallel to XY)

Parallel lines have equal slopes, so slope of \(ZW\) is equal to slope of \(XY\), which is \(-8\).

Matching:

• Side \(WX\): Slope \(\frac{1}{8}\)
• Side \(XY\): Slope \(-8\)
• Side \(YZ\): Slope \(\frac{1}{8}\)
• Side \(ZW\): Slope \(-8\)

Answer:

• Side \(WX\): \(\frac{1}{8}\)
• Side \(XY\): \(-8\)
• Side \(YZ\): \(\frac{1}{8}\)
• Side \(ZW\): \(-8\)