Question

If the point \(\mathrm{P}(6, -3)\) lies on the line segment joining points \(\mathrm{A}(4, 2)\) and \(\mathrm{B}(8, 4)\) then:

Options

• \(\mathrm{AP}=\frac{1}{3} \mathrm{AB}\)

• \(\mathrm{AP}=\frac{1}{4} \mathrm{AB}\)

• \(\mathrm{PB}=\frac{1}{3} \mathrm{AB}\)

• \(\mathrm{AP}=\frac{1}{2} \mathrm{AB}\)

Answer 1

`bb(AP = 1/2 AB)`

Explanation:

The x-coordinate of P gives the fraction \(\frac{AP}{AB} = \frac{6 - 4}{8 - 4} = \frac{1}{2}\) and the y-coordinate confirms it: \(2 + \frac{1}{2}(4 - 2) = 3\). Hence P is the mid-point and \(AP = \frac{1}{2}AB\).