Question

15. What is the distance between the points (4, –7) and (–5, –7)?A. 1 unit B. 3 units C. 7 units D. 9 units

Answer 1

We are given the following two points

`(4,-7)\; \; and\; (-5,-7)`

We are asked to find the distance between these two points.

Recall that the distance formula is given by

`d=\sqrt{\left( {x_2 - x_1 } \right)^2 + \left( {y_2 - y_1 } \right)^2 }`

For the given case, we have

`(x_1,y_1)=(4,-7)\; \; and\; (x_2,y_2)=(-5,-7)`

Let us substitute these points into the above distance formula

`\begin{gathered} d=\sqrt[]{({x_2-x_1})^2+({y_2-y_1})^2} \\ d=\sqrt[]{({-5-4})^2+({-7-(-7)})^2} \\ d=\sqrt[]{({-5-4})^2+({-7+7})^2} \\ d=\sqrt[]{({-9})^2+({0})^2} \\ d=\sqrt[]{81} \\ d=9 \end{gathered}`

Therefore, the distance between the points (4, -7) and (-5, -7) is 9 units.

Option D is the correct answer.