Student Question

Find the distance between the point ( a, 2) and the point (3a,-5) in terms of a.

Expert Answers

An illustration of the letter 'A' in a speech bubbles

The distance between two points (x1, y1) and ( x2, y2) is given as D = sqrt[(x2 - x1)^2 + ( y2 - y1)^2]

Substituting the values we have of the coordinates of the two points we get:

D = sqrt[(3a - a)^2 + ( -5 - 2)^2]

=> D = sqrt [( 2a)^2 + 7^2]

=> D = sqrt (4a^2 + 49)

The required distance between the points is sqrt (4a^2 + 49).

Approved by eNotes Editorial
An illustration of the letter 'A' in a speech bubbles

Given the point (a,2) and the point (3a,-5).

We need to find the distance in terms of a.

We will use the distance between two points formula to calculate.

==> We know that :

D = sqrt[ (x1-x2)^2 + (y1-y2)^2 ]

==> D = sqrt( a-3a)^2 + (2+5)^2]

==> D = sqrt(4a^2 + 49)

Then the distance between the points in terms of a is :

D = sqrt(4a^2+49)

See eNotes Ad-Free

Start your 48-hour free trial to get access to more than 30,000 additional guides and more than 350,000 Homework Help questions answered by our experts.

Get 48 Hours Free Access
Approved by eNotes Editorial