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

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## 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:

\begin{align}{\text{Distance Formula}} = \sqrt {{{\left( {{{\text{x}}_{\text{1}}} - {{\text{x}}_{\text{2}}}} \right)}^2} + {{\left( {{{\text{y}}_{\text{1}}} - {{\text{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}} \qquad \qquad ...\,(1) \\&= \sqrt {{{(36 - 0)}^2} + {{(15 - 0)}^2}} \\ & = \sqrt {{{36}^2} + {{15}^2}} \qquad \text{(By substituting in the 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 $$39\,\rm{km}$$

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