Question

Find the value of a when the distance between the points (3, a) and (4, 1) is $\sqrt{10}$.

Answer 1

The distance d between two points and is given by the formula

The distance between two points (3, a) and (4, 1) is given as. Substituting these values in the formula for distance between two points we have,

Now, squaring the above equation on both sides of the equals sign

Thus we arrive at a quadratic equation. Let us solve this now,

The roots of the above quadratic equation are thus 4 and −2.

Thus the value of ‘a’ could either be.