Question

9. Find the distance between the point P(-12,-2)
and Q(3,6).
Hint: a sketch is useful.​

Answer 1

Distance between points
`P(-12,-2)` and
`Q(3,6)` is 17 units

Explanation:

Given points:

`P(-12,-2)`

`Q(3,6)`

To determine the distance between points P and Q.

Steps to be carried out:

1) Plot the points P and Q on graph.

2) Construct a line from P towards right horizontally and a line from Q downwards vertically such that they meet at point
`O(3,-2)`

3) Join PQ thus forming a right triangle POQ.

4) We can find the distance of sides OP and OQ by counting the units between the points.

OP=
`|-12-3|=|-15|=15\ units`

OQ=
`|6-(-2)|=|6+2|=8\ units`

4)Now, we can apply Pythagorean theorem for triangle POQ.

`PQ^2=OP^2+OQ^2` [
`Hypotenuse^2=Leg1^2+Leg 2^2`]

`PQ^2=15^2+8^2`

`PQ^2=225+64`

`PQ^2=289`

Taking square root both sides:

`√(PQ^2)=√(289)`

`PQ=17\ units` [We take only the positive value as distance is always positive.

∴ Distance between points
`P(-12,-2)` and
`Q(3,6)` is 17 units