Question

The mid-point of the line segment joining (4p, 5) and (2, 3q) is (5, 5p – 1). The values of p and q are respectively are ______.

Options

• \(2, \frac{8}{3}\)

• \(-2, \frac{8}{3}\)

• \(2, \frac{13}{3}\)

• \(-2, \frac{13}{3}\)

Answer 1

The mid-point of the line segment joining (4p, 5) and (2, 3q) is (5, 5p – 1). The values of p and q are respectively are `underlinebb(2, 13/2)`.

Explanation:

\(\frac{4p + 2}{2} = 5\)

\(\Rightarrow p = 2\) 

And then \(\frac{5 + 3q}{2} = 5p - 1 = 9\)

\(\Rightarrow 3q = 13\)

\(\Rightarrow q = \frac{13}{3}\)