Question

Use the Distance Formula to find the distance between each pair of points. Round to the nearest tenth if necessary.

5. P(1, 1), Q(–1, –1)














6. E(1/2,4 1/4),F(5,-1/2)

Answer 1

Given:

The pair of points.

5. P(1, 1), Q(–1, –1)

6.
`E\left((1)/(2),4(1)/(4)\right), F\left(5,-(1)/(2)\right)`

To find:

The distance between the pair of points.

Solution:

Distance formula:

`d=√((x_2-x_1)^2+(y_2-y_1)^2)`

5.

The distance between the pair of points P(1, 1) and Q(–1, –1) is:

`PQ=√((-1-1)^2+(-1-1)^2)`

`PQ=√((-2)^2+(-2)^2)`

`PQ=√(4+4)`

`PQ=√(8)`

`PQ=2√(2)`

Therefore, the distance between P and Q is
`2√(2)`.

6.

The distance between the pair of point
`E\left((1)/(2),4(1)/(4)\right), F\left(5,-(1)/(2)\right)` is:

`EF=\sqrt{\left(5-(1)/(2)\right)^2+\left(-(1)/(2)-4(1)/(4)\right)^2}`

`EF=\sqrt{\left((10-1)/(2)\right)^2+\left(-(1)/(2)-(17)/(4)\right)^2}`

`EF=\sqrt{\left((9)/(2)\right)^2+\left((-2-17)/(4)\right)^2}`

`EF=\sqrt{(81)/(4)+\left((-19)/(4)\right)^2}`

On further simplification, we get

`EF=\sqrt{(81)/(4)+(361)/(16)}`

`EF=\sqrt{(324+361)/(16)}`

`EF=\sqrt{(685)/(16)}`

`EF=√(42.8125 )`

`EF\approx 6.5`

Therefore, the distance between E and F is 6.5 units.