Given the points plotted on the Coordinate Plane:
• You can find the length of the segment BC by finding the distance between the points B and C.
You need to use the formula for calculating the distance between two points:
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
Where the following are the two points:
[tex]\begin{gathered} (x_1,y_1) \\ (x_2,y_2) \end{gathered}[/tex]
In this case, you can identify that:
[tex]\begin{gathered} B(3,-4) \\ C(1,2) \end{gathered}[/tex]
Then, by substituting the corresponding coordinates into the formula and evaluating, you get:
[tex]BC=\sqrt{(1-3)^2+(2-(-4))^2}=\sqrt{40}\text{ }units[/tex]
• You can find the length of the segment FG by finding the distance between the points F and G.
Notice that:
[tex]\begin{gathered} F(-3,-6) \\ G(8,9) \end{gathered}[/tex]
Using the same formula, you get:
[tex]FG=\sqrt{(8-(-3))^2+(9-(-6))^2}=\sqrt{346}\text{ }units[/tex]
• Notice that:
[tex]\begin{gathered} A(-7,5) \\ C(1,2) \end{gathered}[/tex]
Using the same formula, you can find the length of the segment AC:
[tex]AC=\sqrt{(1-(-7))^2+(2-5)^2}=\sqrt{73}\text{ }units[/tex]
• You can identify that:
[tex]\begin{gathered} D(-5,-8) \\ E(-8,-9) \end{gathered}[/tex]
Then, the length of the segment DE is:
[tex]DE=\sqrt{(-8-(-5))^2+(-9-(-8))^2}=\sqrt{10}\text{ }units[/tex]
• Notice that:
[tex]B(3,-4)[/tex]
Then, the length of the segment AB is:
[tex]AB=\sqrt{(3-(-7))^2+(-4-5)^2}=\sqrt{181}\text{ }units[/tex]
• You can find the length of the segment EF:
[tex]EF=\sqrt{(-3-(-8))^2+(-9-(-6))^2}=\sqrt{34}\text{ }units[/tex]
Hence, the answer is:
