Question

Determine the values of n
P(3n, n-7), Q(4n, n + 5), PQ = 13

Answer 1

To determine the values of n, we can use the distance formula to find the length of the line segment PQ.

The distance formula is given by:

d = √((x2 - x1)^2 + (y2 - y1)^2)

Let's substitute the given coordinates into the distance formula:

13 = √((4n - 3n)^2 + (n + 5 - (n - 7))^2)

Simplifying the expression inside the square root:

13 = √(n^2 + (12)^2)

Square both sides of the equation:

13^2 = n^2 + 144

169 = n^2 + 144

Rearrange the equation:

n^2 = 169 - 144

n^2 = 25

Take the square root of both sides of the equation:

n = ±5

Therefore, the values of n are 5 and -5.

Explanation: