Question

Find distance between points (a, b) (-a,-b)

Answer 1

Let the coordinates be P(a,b) Q(-a,-b)
Now ,using distance formula
PQ = root over (a+a)² + (b+b)²
= root over 4a² + 4b²
= root over 4(a²+b²)
= 2 root over a² + b²

Answer 2

$\huge \underline \mathfrak {Solution:-}$

We have to find out the distance between the two points (a.b) and (-a,-b).

For finding the distance between two points we can use the given formula.

Distance $= \sqrt{ {(x_1 - x_2)}^{2} + {(y_1 - y_2)}^{2} }$

This formula is used to find out the distance between two points and that's why it is named as distance formula.

According to question,

$x_1 = a \\ \\ x_2 = -a \\ \\ y_1 = b\\ \\ y_2 = -b$

Now,

Distance $= \sqrt{ {(x_1 - x_2)}^{2} + {(y_1 - y_2)}^{2} }$

$= \sqrt{ {(a-(-a))}^{2} + {( b-(-b))}^{2} } \\ \\ = \sqrt{ {( a+a)}^{2} + { (b+b)}^{2} } \\ \\ = \sqrt{ {(2a)}^{2} + {(2b)}^{2} } \\ \\ = 2\sqrt{ a^{2}+b^{2}} \: units$