Find the distance between the following pair of points. R(0, -3), S(0, 5/2)
Find the distance between the following pair of points. R(0, -3), S(0, 5/2)
Suppose co-ordinates of point R are (x1 , y1) and of point S are (x2, y2).
x1 = 0, y1 = -3, x2 = 0, y2 = `5/2`
According to distance formula,
\[=d(R, S) \sqrt{(x_2 – x_1)^2 + (y_2 – y_1)^)}\]
\[=d(R, S) \sqrt{((0 – 0)^2 + [5/2 – (- 3)]^2)}\]
\[=d(R, S)\sqrt{((0)^2 + [5/2 + 3]^2)}\]
\[=d(R, S) \sqrt{((0)^2 + (11/2)^2)}\]
\[=d(R, S)\sqrt{(0 + 121/4)}\]
\[=d(R, S) \sqrt{(121/4)}\]
d(R, S) =11/2
∴ distance between points R and S is 11/2.
Explanation:-
We can use the distance formula to find the distance between two points in a coordinate plane. The distance formula is:
distance = sqrt((x2 – x1)^2 + (y2 – y1)^2)
Substituting the given values, we get:
distance = sqrt((0 – 0)^2 + ((5/2) – (-3))^2)
distance = sqrt(0 + (5/2 + 6/2)^2)
distance = sqrt(121/4)
distance = 11/2
Therefore, the distance between the points R(0, -3) and S(0, 5/2) is 11/2 units.