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:

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

a.

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

$AB=\sqrt{(-3-(-6))^2+((-1-(-4))^2}$

$AB=\sqrt{(3)^2+(3)^2}$

$AB=\sqrt{2(3)^2}$

$AB=3\sqrt{2}$

$AB\approx 4.2$

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:

$CD=\sqrt{(-4-3.5)^2+(2.5-1)^2}$

$CD=\sqrt{(-7.5)^2+(1.5)^2}$

$CD=\sqrt{56.25+2.25 }$

$CD=\sqrt{58.5 }$

$CD\approx 7.6$

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:

$XY=\sqrt{(-5-5)^2+(5-(-5))^2}$

$XY=\sqrt{(-10)^2+(10)^2}$

$XY=\sqrt{100+100}$

$XY=\sqrt{200}$

$XY\approx 14.1$

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