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Questions
Find the distance between the following pairs of points:
(2, 3), (4, 1)
Find the distance between the following pairs of points:
A (2, 3), B (4, 1)
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Solution 1
l = `sqrt((x_2 - x_1)^2 + (y_2 - y_1)^2)`
= `sqrt((4 - 2)^2 + (1 - 3)^2)`
= `sqrt(2^2 + (- 2)^2)`
= `sqrt(4 + 4)`
= `sqrt(8)`
= `sqrt(4 × 2)`
= `2sqrt(2)` units
Solution 2
A (2, 3), B (4, 1)
Suppose the coordinates of point A are (x1, y1) and those of point B are (x2, y2).
x1 = 2, y1 = 3, x2 = 4, y2 = 1
According to distance formula,
d(A,B) = `sqrt((x_2 - x_1)^2 + (y_2 - y_1)^2)`
d(A,B) = `sqrt((4 - 2)^2 + (1 - 3)^2)`
d(A,B) = `sqrt(2^2 + (- 2)^2)`
d(A,B) = `sqrt(4 + 4)`
d(A,B) = `sqrt(8)`
d(A,B) = `sqrt(4 × 2)`
d(A,B) = `2sqrt(2)`
The distance between points A and B is `2sqrt(2)` units.
RELATED QUESTIONS
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Calculate the distance between A (7, 3) and B on the x-axis whose abscissa is 11.
KM is a straight line of 13 units If K has the coordinate (2, 5) and M has the coordinates (x, – 7) find the possible value of x.
Find distance between point Q(3, –7) and point R(3, 3)
Solution: Suppose Q(x1, y1) and point R(x2, y2)
x1 = 3, y1 = –7 and x2 = 3, y2 = 3
Using distance formula,
d(Q, R) = `sqrt(square)`
∴ d(Q, R) = `sqrt(square - 100)`
∴ d(Q, R) = `sqrt(square)`
∴ d(Q, R) = `square`
Show that the point (0, 9) is equidistant from the points (–4, 1) and (4, 1).
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Case Study -2
A hockey field is the playing surface for the game of hockey. Historically, the game was played on natural turf (grass) but nowadays it is predominantly played on an artificial turf.
It is rectangular in shape - 100 yards by 60 yards. Goals consist of two upright posts placed equidistant from the centre of the backline, joined at the top by a horizontal crossbar. The inner edges of the posts must be 3.66 metres (4 yards) apart, and the lower edge of the crossbar must be 2.14 metres (7 feet) above the ground.
Each team plays with 11 players on the field during the game including the goalie. Positions you might play include -
- Forward: As shown by players A, B, C and D.
- Midfielders: As shown by players E, F and G.
- Fullbacks: As shown by players H, I and J.
- Goalie: As shown by player K.
Using the picture of a hockey field below, answer the questions that follow:
What are the coordinates of the position of a player Q such that his distance from K is twice his distance from E and K, Q and E are collinear?
Find the points on the x-axis which are at a distance of `2sqrt(5)` from the point (7, – 4). How many such points are there?
The distance of the point (5, 0) from the origin is ______.
