# Ex.7.1 Q2 Coordinate Geometry Solution - NCERT Maths Class 10

## Question

Find the distance between the points \((0, 0)\) and \((36, 15)\). Can you now find the distance between the two towns \(A\) and \(B\) discussed in Section 7.2?

## Text Solution

**Reasoning:**

The distance between the two points can be measured using the Distance Formula which is given by:

Distance Formula

\[\begin{align}= \sqrt {{{\left( {{x_{\text{1}}} - {x_{\text{2}}}} \right)}^2} + {{\left( {{y_{\text{1}}} - {y_{\text{2}}}} \right)}^2}} .\end{align}\]

**What is Known?**

The \(x\) and \(y\) co-ordinates of the points between which the distance is to be measured.

**What is Unknown?**

The distance between the towns \(A\) and \(B\).

**Steps:**

Given:

Let the points be \(A(0,0)\) and \(B(36,15)\)

Hence,

- \(x_1 = 0\)
- \(y_1 = 0\)
- \(x_2 = 36\)
- \(y_2 =15\)

We know that the distance between the two points is given by the Distance Formula,

\[\begin{align}&\sqrt {{{\left( {{x_1} - {x_2}} \right)}^2} + {{\left( {{y_1} - {y_2}} \right)}^2}} ...\,(1) \\&= \sqrt {{{(36 - 0)}^2} + {{(15 - 0)}^2}} \\

& = \sqrt {{{36}^2} + {{15}^2}} \\& \text{[By substituting in equation (1)}]\\\\

& = \sqrt {1296 + 225} \\

&= \sqrt {1521} \\

&= 39\end{align}\]

Yes, it is possible to find the distance between the given towns \(A\) and \(B\).

The positions of the towns \(A\) & \(B\) are given by \((0, 0)\) and \((36, 15)\), hence, as calculated above, the distance between town \(A\) and \(B\) will be \(39\,\rm{km}\)