Question

Determine the measure of each segment then indicate whether the statements are true or false

Answer 1

Answer:

$d_{AB}\ne d_{JK}$

$d_{AB}\ne \:d_{GH}$

$d_{GH}\ne \:d_{JK}$

Therefore,

Option (A) is false

Option (B) is false

Option (C) is false

Step-by-step explanation:

Considering the graph

Given the vertices of the segment AB

• A(-4, 4)

• B(2, 5)

Finding the length of AB using the formula

$d_{AB}\:=\:\sqrt{\left(x_2-x_1\right)^2+\left(y_2-y_1\right)^2}$

        $=\sqrt{\left(2-\left(-4\right)\right)^2+\left(5-4\right)^2}$

         $=\sqrt{\left(2+4\right)^2+\left(5-4\right)^2}$

         $=\sqrt{6^2+1}$

         $=\sqrt{36+1}$

        $=\sqrt{37}$

$d_{AB}\:=\sqrt{37}$

$d_{AB}=6.08$ units        

Given the vertices of the segment JK

• J(2, 2)

• K(7, 2)

From the graph, it is clear that the length of JK = 5 units

so

$d_{JK}=5$ units

Given the vertices of the segment GH

• G(-5, -2)

• H(-2, -2)

Finding the length of GH using the formula

$d_{GH}\:=\:\sqrt{\left(x_2-x_1\right)^2+\left(y_2-y_1\right)^2}$

         $=\sqrt{\left(-2-\left(-5\right)\right)^2+\left(-2-\left(-2\right)\right)^2}$

          $=\sqrt{\left(5-2\right)^2+\left(2-2\right)^2}$

          $=\sqrt{3^2+0}$

           $=\sqrt{3^2}$

$\mathrm{Apply\:radical\:rule\:}\sqrt[n]{a^n}=a,\:\quad \mathrm{\:assuming\:}a\ge 0$

$d_{GH}\:=\:3$ units

Thus, from the calculations, it is clear that:

$d_{AB}=6.08$  

$d_{JK}=5$

$d_{GH}\:=\:3$

Thus,

$d_{AB}\ne d_{JK}$

$d_{AB}\ne \:d_{GH}$

$d_{GH}\ne \:d_{JK}$

Therefore,

Option (A) is false

Option (B) is false

Option (C) is false