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 \(39\,\rm{km}\)