Question

In what ratio is the line joining the points (2, –3) and (5, 6) divided by the x-axis. -Maths 9th

Answer 1

(b) (2, 1) (– 2, 1)Let PQRS be the required square and P(0, –1) and R(0, 3) be its two opposite vertices. Length of diagonal PR = \(\sqrt{(0-0)^2+(3+1)^2}\) = \(\sqrt{16}\) = 4∴ Length of each side = \(rac{ ext{diagonal}}{\sqrt2}\) = \(rac{4}{\sqrt2}\) = \(2\sqrt2.\)Let the co-ordinates of another vertex of the square say Q be (a, b) ∴ Its distance from vertex P should be equal to its distance from vertex R.∴ \(\sqrt{(a-0)^2+(b+1)^2}\) = \(\sqrt{(a-0)^2+(b-3)^2}\)⇒ a2 + b2 + 2b + 1 = a2 + b2 – 6b + 9 ⇒ 8b = 8 ⇒ b = 1 Also, this distance QP = \(2\sqrt2\) ∴ \(\sqrt{(a-0)^2+(b+1)^2}\) = \(2\sqrt2\)⇒ a2 + b2 + 2b + 1 = 8 ⇒ a2 + 4 = 8 ⇒ a2 = 4 ⇒ a = ± 2. ∴ The other two vertices of the square are (+2, 1) and (–2, 1).