Question

the points ( i(6, -5) ), ( j(8, -2) ), ( k(5, 2) ), and ( l(0, -1) ) form a quadrilateral. find the desired slopes and lengths, then fill in the words that best identifies the type of quadrilateral.
answer attempt 1 out of 2
slope of ( overline{ij} = )
length of ( overline{ij} = )
slope of ( overline{jk} = )
length of ( overline{jk} = )
slope of ( overline{kl} = )
length of ( overline{kl} = )
slope of ( overline{li} = )
length of ( overline{li} = )
quadrilateral ( ijkl ) is

Explanation:

Step1: Calculate slope of $\overline{IJ}$

Slope formula: $m=\frac{y_2-y_1}{x_2-x_1}$
$m_{\overline{IJ}}=\frac{-2-(-5)}{8-6}=\frac{3}{2}$

Step2: Calculate length of $\overline{IJ}$

Distance formula: $d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$
$d_{\overline{IJ}}=\sqrt{(8-6)^2+(-2-(-5))^2}=\sqrt{2^2+3^2}=\sqrt{13}$

Step3: Calculate slope of $\overline{JK}$

$m_{\overline{JK}}=\frac{2-(-2)}{5-8}=\frac{4}{-3}=-\frac{4}{3}$

Step4: Calculate length of $\overline{JK}$

$d_{\overline{JK}}=\sqrt{(5-8)^2+(2-(-2))^2}=\sqrt{(-3)^2+4^2}=\sqrt{25}=5$

Step5: Calculate slope of $\overline{KL}$

$m_{\overline{KL}}=\frac{-1-2}{0-5}=\frac{-3}{-5}=\frac{3}{2}$

Step6: Calculate length of $\overline{KL}$

$d_{\overline{KL}}=\sqrt{(0-5)^2+(-1-2)^2}=\sqrt{(-5)^2+(-3)^2}=\sqrt{34}$

Step7: Calculate slope of $\overline{LI}$

$m_{\overline{LI}}=\frac{-5-(-1)}{6-0}=\frac{-4}{6}=-\frac{2}{3}$

Step8: Calculate length of $\overline{LI}$

$d_{\overline{LI}}=\sqrt{(6-0)^2+(-5-(-1))^2}=\sqrt{6^2+(-4)^2}=\sqrt{52}=2\sqrt{13}$

Step9: Classify the quadrilateral

Only $\overline{IJ} \parallel \overline{KL}$ (equal slopes), so it is a trapezoid.

Answer:

slope of $\overline{IJ}$ = $\frac{3}{2}$
length of $\overline{IJ}$ = $\sqrt{13}$
slope of $\overline{JK}$ = $-\frac{4}{3}$
length of $\overline{JK}$ = $5$
slope of $\overline{KL}$ = $\frac{3}{2}$
length of $\overline{KL}$ = $\sqrt{34}$
slope of $\overline{LI}$ = $-\frac{2}{3}$
length of $\overline{LI}$ = $2\sqrt{13}$
Quadrilateral IJKL is a trapezoid