Question

What is the sum of the distances of R to Q and P to Q?

Answer 1

The sum of the distances of R to Q and P to Q is 9 units.

Solution:

Given points are P(–3, 6), Q(3, 6) and R(3, 3).

Distance between two points formula:

`√((x_2-x_1)^2+(y_2-y_1)^2)`

Distance from R to Q:

Here
`x_1=3, y_1=3, x_2=3, y_2=6`

Substitute these in the given formula, we get

Distance =
`√((3-3)^2+(6-3)^2)`

`=√(0+9)`

= 3 units

Distance from R to Q is 3 units.

Distance from P to Q:

Here
`x_1=-3, y_1=6, x_2=3, y_2=6`

Substitute these in the given formula, we get

Distance =
`√((3-(-3))^2+(6-6)^2)`

`=√(36+0)`

= 6 units

Distance from P to Q is 6 units.

Sum of the distances = 3 + 6 = 9 units

Hence the sum of the distances of R to Q and P to Q is 9 units.