Question

Show that the point (7,1) lies on the perpendicular bisector of the line joining (2,4) and (4,6)​

Answer 1

Answer: True

Explanation:

Let the point (7, 1) be Point A

Let the perpendicular bisector of the line joining (2,4) and (4,6) be Line PQ; P(2, 4) and Q(4, 6)

If A (7,1) lies on perpendicular bisector of P(2,4) and Q (4, – 6), then AP=AQ

`\begin{aligned}\therefore \quad A P &=√(\left(2-7\right)^2+\left(4-1\right)^2)\:\\&=√(5^2+3^2)\\&=√(25+9)=√(34) \\\mathrm{and} \ \ \ A &=√(\left(4-7\right)^2+\left(6-1\right)^2)\: \\&=√(3^2+5^2) \\&=√(9+25)=√(34)\end{aligned}`

Therefore, (7, 1) does lie on the perpendicular bisector of the line joining (2,4) and (4,6)​