## Problem 512

What is the distance between points P(10, 7) and Q(1, 8)?

Solution:-

Use the Distance Formula

## Problem 511

What is the distance between points P(6, -2) and Q(3, 4)?

Solution:-

Use the Distance Formula

## Problem 510

What is the distance between P(0, 0) and Q(5, 12)?

Solution:-

Use the Distance Formula

d = 13

## Problem 509

What is the distance between P(7, 0) and Q(8, 0)?

Solution:-

Use the Distance Formula

d  = 1

## Find the distance between the pair of points.

Find  the distance between the pair of points.

Give an exact answer and an approximation to three decimal places.

(-5,6) and (2, -3)

Solution:-

To find the distance between two points, use the distance formula below.

d =  .

Substitute the value and calculate.

d =

=

=

This is the exact value of the distance between the two point.

Now find the approximate distance to three decimal places.

11.402

## Distance Formula

Distance Formula

The distance between the points (x1, y1) and (x2, y2) is

d = .

## Distance between Two points (Two Dimensions)

Distance between Two points (Two Dimensions) :

Let and are two points in a plane,distance between them is .

Now we have to find the distance , draw two perpendiculars on axes from P and Q points, which are PM and QN, now draw a perpendicular PR from point P on QN.

According to the above figure:

OM = ; PM =

ON = ; QN =

So PR = MN = ON – OM =

And QR = QN – RN  = QN – PM =

Now In right triangle PRQ :

PQ =

Or PQ =

Or d =   ….( distance formula)