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)

Question

asked Nov 25, 2022 114k views

1 Answer

Cube Drone · Answer 1 · 2022-11-30T05:37:22+0000

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
.

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.