Question

I need help! (HAPPY MLK DAY!!!)

Answer 1

The slope and length of the given sides of the quadrilateral can be

found by using the coordinates of the vertices.

Correct responses:

• $Slope \ of \ \overline{IJ} = \underline{-\dfrac{7}{6} }$,      Length of $\overline{IJ}$ = $\underline{\sqrt{85} }$

• $Slope \ of \ \overline{JK} = \underline {-\dfrac{2}{9}}$,     Length of $\overline{JK}$ = $\underline{\sqrt{85} }$

• $Slope \ of \ \overline{KL} = \underline{-\dfrac{7}{6} }$,      Length of $\overline{KL}$ = $\underline{\sqrt{85}}$

• $Slope \ of \ \overline{LI} = \underline{ -\dfrac{2}{9} }$,        Length of $\overline{LI}$ = $\underline{\sqrt{85} }$

Methods used to find the slope and length of a line

The given coordinates of the vertices are;

K(-7, 0), J(2, -2), I(8, -9), L(-1, -7)

• $Slope = \mathbf{\dfrac{y_2 - y_1}{x_2 - x_1}}$

• $Length \ of \ line = \mathbf{ \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}}$

Therefore;

$Slope \ of \ \mathbf{\overline{IJ}} = \dfrac{-2 - (-9)}{2 - 8} = \dfrac{7}{-6} = \underline{ -\dfrac{7}{6}}$

$Length \ of \ \mathbf{\overline{IJ}} = \sqrt{(2 - 8)^2 + (-2 - (-9))^2} = \underline{\sqrt{85}}$

$Slope \ of \ \mathbf{\overline{JK}} = \dfrac{0 - (-2)}{-7 - 2} = \dfrac{2}{-9} = \underline{-\dfrac{2}{9}}$

$Length \ of \ \mathbf{\overline{JK}} = \sqrt{(-7 - 2)^2 + (0 - (-2))^2} = \underline{ \sqrt{85}}$

$Slope \ of \ \mathbf{\overline{KL}} = \dfrac{0 - (-7)}{-7 - (-1)} = \dfrac{7}{-6} = \underline{ -\dfrac{7}{6}}$

$Length \ of \ \mathbf{\overline{KL} }= \sqrt{(-7 - (-1))^2 + (0 - (-7))^2} =\underline{ \sqrt{85}}$

$Slope \ of \ \mathbf{\overline{LI}} = \dfrac{(-9 - (-7))}{(8 - (-1))} = \dfrac{-2}{9} = \underline{-\dfrac{2}{9}}$

$Length \ of \ \mathbf{\overline{LI}} = \sqrt{(8 - (-1))^2 + (-9 - (-7))^2} = \underline{\sqrt{85}}$

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