Question

3 Which of the following pairs of points has a distance of 9 units between them? Select three that apply. A. Point R at (4.-7) and Point Wat (-5, -7) B. Point N at (5, 8) and Point Z at (5, 1) C. Point l at (3, 10) and Point J at (3, 1) D. Point G at (1, 3) and Point Q at (I, 6)

Answer 1

Now let's solve using the distance formula below:

`d\text{ = }\sqrt[]{(x_{2\text{ - }}x_1)^2+(y_{2\text{ - }}y_1)^2}`

The points are represented as: (x1, y1) and (x2, y2)

For A:

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

For B:

`\begin{gathered} d\text{ = }\sqrt[]{(5-5)^2+(1-8)^2} \\ =\text{ }\sqrt{0\text{ + (49)}} \\ =7 \\ \end{gathered}`

For C:

`\begin{gathered} d\text{ = }√((3-3)^2+(1-10)^2) \\ =\text{ }√(0+(-9)^2) \\ =√(81) \\ =\text{ 9} \end{gathered}`

For D:

`\begin{gathered} d\text{ = }√((1-1)^2+(6-3)^2) \\ =\text{ }√(0+(3)^2) \\ =\text{ }√(9) \\ =\text{ 3} \end{gathered}`

From the calculations, we can see the pairs that have the distance of 9 between them are only otion A and C:

A. Point R at (4.-7) and Point W at (-5, -7)

C. Point l at (3, 10) and Point J at (3, 1)