Question

1. find the exact simplified (no decimals) length of each segment below. which segments are congruent? ab = jx = gh =

Explanation:

Step1: Recall distance formula

The distance formula between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$.

Step2: Find length of $\overline{AB}$

Let $A=(0,5)$ and $B=(6,4)$. Then $d_{AB}=\sqrt{(6 - 0)^2+(4 - 5)^2}=\sqrt{36+1}=\sqrt{37}$.

Step3: Find length of $\overline{JX}$

Let $J=(- 1,1)$ and $X=(6,2)$. Then $d_{JX}=\sqrt{(6+1)^2+(2 - 1)^2}=\sqrt{49 + 1}=\sqrt{50}=5\sqrt{2}$.

Step4: Find length of $\overline{GH}$

Let $G=(1,7)$ and $H=(2,0)$. Then $d_{GH}=\sqrt{(2 - 1)^2+(0 - 7)^2}=\sqrt{1 + 49}=\sqrt{50}=5\sqrt{2}$.

Step5: Compare lengths

Since $d_{JX}=5\sqrt{2}$ and $d_{GH}=5\sqrt{2}$, $\overline{JX}$ and $\overline{GH}$ are congruent.

Answer:

$AB=\sqrt{37}$, $JX = 5\sqrt{2}$, $GH=5\sqrt{2}$; $\overline{JX}$ and $\overline{GH}$ are congruent.