Verified answer

[tex]\Large\mathbb{SOLUTION:}[/tex]

Statement: A new transmission tower will be put up midway between two existing towers. On a map drawn on a coordinate plane, the coordinates of first existing tower are (-5, -3) and the coordinates of the second existing tower are (9, 13).

Required: What are the coordinates of the point where the new tower will be placed?

Let,

• [tex]\sf{(x_1, \: y_1) = (-5, \: -3)}[/tex]
• [tex]\sf{(x_2, \: y_2) = (9, \: 13)}[/tex]

[tex]\bold{Formula : } \qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad \\ \boxed{ \rm \: Midpoint = \bigg( \dfrac{x_1 + x_2}{2}, \: \dfrac{y_1 + y_2}{2} \bigg) \: } [/tex]

Substitute the given values into the above formula and solve for Midpoint:

[tex]\sf:\implies{Midpoint = \bigg(\dfrac{x_1 + x_2}{2}, \: \dfrac{y_1 + y_2}{2} \bigg)}[/tex]

[tex]\sf:\implies{Midpoint = \bigg( \dfrac{ - 5 + 9}{2}, \: \dfrac{ - 3 + 13}{2}\bigg)}[/tex]

[tex]\sf:\implies{Midpoint = \bigg(\dfrac{4}{2}, \: \dfrac{10}{2} \bigg)}[/tex]

[tex]\sf:\implies{Midpoint = \bigg(2, \: 5 \bigg)} \\ [/tex]

Therefore, the coordinates of the point where the new tower will be placed is (2, 5).