Question

There are two routes to travel from the place A to B by bus. The first bus reaches the place B via C and the second bus reaches the place B from A directly. The position of A, B and C are represented in the following graph.

Based on the above information, answer the following questions.

Suppose if C is the place on the y-axis which is equidistant from the places A(-5,-2) and B(3, 2), then CA = ___ km.

• A. 5
• B. 4
• C. 3
• D. 2

Answer 1

The correct option is A 5

Given, A(-5, -2), B(3, 2).
Let, the coordinates of C be (0, y)
We have,
CA = CB
$\Rightarrow C{A}^2=C{B}^2\Rightarrow (-5-0{)}^2+(-2-y{)}^2=(3-0{)}^2+(2-y{)}^2\Rightarrow 25+4+y^2+4y=9+4+y^2-4y\Rightarrow 8y=-16\Rightarrow y=-2$

Therefore coordinates of C is (0, -2)

By distance formula,
$\text{CA}=\sqrt{(-5-0{)}^2+(-2+2{)}^2}=\sqrt{25}=5km$