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