Question

Use the distance formula to find the distance between each pair of points round to the nearest 10th if necessary

Answer 1

Given:

The pairs of points are:

a. A(-6,-4), B(-3,-1)

b. C(3.5,1), D(-4,2.5)

c. X(5,-5), Y(-5,5)

To find:

The distance between the pair of points by using the distance formula.

Solution:

Distance formula:

`d=√((x_2-x_1)^2+(y_2-y_1)^2)`

a.

Using the distance formula, the distance between the points A(-6,-4) and B(-3,-1) is:

`AB=√((-3-(-6))^2+((-1-(-4))^2)`

`AB=√((3)^2+(3)^2)`

`AB=√(2(3)^2)`

`AB=3√(2)`

`AB\approx 4.2`

Therefore, the distance between the points A(-6,-4) and B(-3,-1) is about 4.2 units.

b.

Using the distance formula, the distance between the points C(3.5,1) and D(-4,2.5) is:

`CD=√((-4-3.5)^2+(2.5-1)^2)`

`CD=√((-7.5)^2+(1.5)^2)`

`CD=√(56.25+2.25 )`

`CD=√(58.5 )`

`CD\approx 7.6`

Therefore, the distance between the points C(3.5,1) and D(-4,2.5) is about 7.6 units.

c.

Using the distance formula, the distance between the points X(5,-5) and Y(-5,5) is:

`XY=√((-5-5)^2+(5-(-5))^2)`

`XY=√((-10)^2+(10)^2)`

`XY=√(100+100)`

`XY=√(200)`

`XY\approx 14.1`

Therefore, the distance between the points X(5,-5) and Y(-5,5) is about 14.1 units.