Question

8The coordinates ofpoint A are (-6, 4). The coordinates ofpoint B are (3, 4)>Which expressionrepresents thedistance, in units,between points Aand B ?

Answer 1

Given the following coordinates of A and B below,

`\begin{gathered} A(x_1,y_1)=(-6,4) \\ B(x_2,y_2)=(3,4) \end{gathered}`

To find the distance between coordinates A and B, the formula is,

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

Substituting the points into the formula given above,

`\begin{gathered} d=\sqrt[]{(3-(-6)^2+(4-4)^2} \\ d=\sqrt[]{9^2+0^2}=\sqrt[]{81+0}=\sqrt[]{81}=9\text{ units} \end{gathered}`

Since the distance between the two points is 9 units,

`\begin{gathered} \lvert-6\rvert\text{ is 6 because the absolute value of a number is always positive} \\ \lvert3\rvert\text{ is} \\ \lvert-6\rvert+\lvert3\rvert=9\text{ units} \end{gathered}`

Hence, A is the right option.