Question

Find the distance between the points R (-3, 0), S $\left( {0,\dfrac{5}{2}} \right)$.

Answer 1

Hint: In the above question of coordinate geometry, we have two points R and S whose co- ordinates are given. To find the distance between the points we will use a simple formula $D = \sqrt {{{({x_2} - {x_1})}^2} + {{({y_2} - {y_1})}^2}} $where ${x_1}$= -3, ${y_1}$= 0, ${x_2}$= 0, and ${y_2}$= $\dfrac{5}{2}$.

Complete step-by-step answer:
Given points R (-3, 0) and S $\left( {0,\dfrac{5}{2}} \right)$.
To determine the distance between two points with the coordinates$({x_1},{y_1})$and $\left( {{x_2},{y_2}} \right)$ is $D = \sqrt {{{({x_2} - {x_1})}^2} + {{({y_2} - {y_1})}^2}} $.
Here, ${x_1}$= -3, ${y_1}$= 0, ${x_2}$= 0, and ${y_2}$= $\dfrac{5}{2}$
Now, Distance between the points R and S $ = \sqrt {{{({x_2} - {x_1})}^2} + {{({y_2} - {y_1})}^2}} $
$ = \sqrt {{{\left( {0 - ( - 3)} \right)}^2} + {{\left( {\dfrac{5}{2} - 0} \right)}^2}} $
$ = \sqrt {9 + \dfrac{{25}}{4}} = \dfrac{{\sqrt {61} }}{2}$$ = \dfrac{{7.81}}{2} = 3.90$units
Therefore, the distance between the points R (-3, 0), S $\left( {0,\dfrac{5}{2}} \right)$ is 3.90 units.

The distance between the two points is $3.90$units.

Note: Concept of coordinate geometry is also known as Cartesian geometry. Coordinate geometry shows the link between geometry and algebra. It is a part of geometry where positions of points on the plane are expressed using an ordered pair of numbers. Coordinates are the set of values which shows the exact position of point on the plane. Points are placed on the “coordinate plane”. It has two scales – x – axis and y – axis. The points where the axes cross is called origin where x and y both are zero. On the x – axis, values to the right are positive and values to the left are negative. On the y – axis, values above the origin are positive and values below the origin are negative. The location of points expressed in two numbers for example R (-3, 2) where -3 shows where it is on x – axis and 2 shows where it is on y – axis.