Question

# Distance between the two points (0,7) and ( - 7,0) is${\text{(a) }}2\sqrt 7 ${\text{(b) }}7\sqrt 2$ {\text{(c) }}\sqrt {14}$${\text{(d) }} + 1$

Hint: Use the variant of Pythagorean theorem i.e. distance formula to find the distance between the given two points.

We know that the distance between any two points $A({x_1},{y_1})$ and $B({x_2},{y_2})$ is given by the distance formula:

${\text{Distance }}d = \sqrt {{{({x_2} - {x_1})}^2} + {{({y_2} - {y_1})}^2})}$.............................(1)

Here let A(0,7) and B(- 7,0), then we get the distance between 2 points by substituting the values in equation (1),

$d = {\sqrt {{{( - 7 - 0)}^2} + {{(0 - 7)}^2}} ^{}}$

$d = {\sqrt {{{( - 7)}^2} + {{( - 7)}^2}} ^{}}$

$d = \sqrt {{{(7)}^2} + {{(7)}^2}}$

$d = \sqrt {{{(7)}^2}(1 + 1)}$

$d = \sqrt {{{(7)}^2}(2)}$

$d = 7\sqrt 2$

Therefore, the distance between the two points (0,7) and ( - 7,0) is $7\sqrt 2$ which is option (b).

Note: The number of points between which the distance is to be calculated, must be observed carefully and then use the distance formula. The alternative method to solve this problem is by using Pythagoras theorem. First mark the points on the sheet and join them, later find the length of the horizontal and vertical line from the given points and by using the Pythagoras theorem we will find the length of the third line which gives us the distance between two points.