graph the quadrilateral on graph paper, then answer the questions. the vertices of quadrilateral abcd are: ( a(1,5) ) ( b(-2,8) ) ( c(-8,2) ) ( d(-5,-1) ) what is the length of each diagonal?

Question

Accepted Answer

# Explanation:
## Step1: Find the length of diagonal $AC$
Use the distance formula $d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$. For points $A(1,5)$ and $C(-8,2)$, $x_1 = 1,y_1=5,x_2=-8,y_2 = 2$.
$$
\begin{align*}
d_{AC}&=\sqrt{(-8 - 1)^2+(2 - 5)^2}\
&=\sqrt{(-9)^2+(-3)^2}\
&=\sqrt{81 + 9}\
&=\sqrt{90}\
&=3\sqrt{10}\approx9.49
\end{align*}
$$
## Step2: Find the length of diagonal $BD$
For points $B(-2,8)$ and $D(-5,-1)$, $x_1=-2,y_1 = 8,x_2=-5,y_2=-1$.
$$
\begin{align*}
d_{BD}&=\sqrt{(-5+2)^2+(-1 - 8)^2}\
&=\sqrt{(-3)^2+(-9)^2}\
&=\sqrt{9+81}\
&=\sqrt{90}\
&=3\sqrt{10}\approx9.49
\end{align*}
$$

# Answer:
The length of diagonal $AC$ is $3\sqrt{10}\approx9.49$ and the length of diagonal $BD$ is $3\sqrt{10}\approx9.49$

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QUESTION IMAGE

Question

Explanation:

Step1: Find the length of diagonal \(AC\)

Step2: Find the length of diagonal \(BD\)

Answer: