Question

i need help! (HAPPY MLK DAY!!!)
The drop down is in gray
its filling in the blank for this "Quadrilateral IJKL can BEST be described as.....

please help! I'm not that great with slopes!!!

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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