Advertisements
Advertisements
Question
Find distance between point A(–1, 1) and point B(5, –7):
Solution: Suppose A(x1, y1) and B(x2, y2)
x1 = –1, y1 = 1 and x2 = 5, y2 = –7
Using distance formula,
d(A, B) = `sqrt((x_2 - x_1)^2 + (y_2 - y_1)^2`
∴ d(A, B) = `sqrt(square +[(-7) + square]^2`
∴ d(A, B) = `sqrt(square)`
∴ d(A, B) = `square`
Advertisements
Solution
Suppose A(x1, y1) and B(x2, y2)
x1 = –1, y1 = 1 and x2 = 5, y2 = – 7
Using distance formula,
d(A, B) = `sqrt((x_2 - x_1)^2 + (y_2 - y_1)^2`
∴ d(A, B) = \[\sqrt{\boxed{[5 - (-1)]^2} + [(-7) + \boxed{-1}]^2}\]
∴ d(A, B) = `sqrt(6^2 + (-8)^2`
∴ d(A, B) = `sqrt(36 + 64)`
∴ d(A, B) = \[\sqrt{\boxed{100}}\]
∴ d(A, B) = \[\boxed{10 \phantom{.}\text{units}}\]
APPEARS IN
RELATED QUESTIONS
In a classroom, 4 friends are seated at the points A, B, C and D as shown in the following figure. Champa and Chameli walk into the class and after observing for a few minutes, Champa asks Chameli, “Don’t you think ABCD is a square?” Chameli disagrees.
Using distance formula, find which of them is correct.

Name the type of quadrilateral formed, if any, by the following point, and give reasons for your answer:
(4, 5), (7, 6), (4, 3), (1, 2)
Find the distance between the following pair of points:
(-6, 7) and (-1, -5)
If A (-1, 3), B (1, -1) and C (5, 1) are the vertices of a triangle ABC, find the length of the median through A.
Find the distance between the points
(ii) A(7,-4)and B(-5,1)
AB and AC are the two chords of a circle whose radius is r. If p and q are
the distance of chord AB and CD, from the centre respectively and if
AB = 2AC then proove that 4q2 = p2 + 3r2.
Find the relation between x and y if the point M (x,y) is equidistant from R (0,9) and T (14 , 11).
Prove taht the points (-2 , 1) , (-1 , 4) and (0 , 3) are the vertices of a right - angled triangle.
Prove that the points (0 , -4) , (6 , 2) , (3 , 5) and (-3 , -1) are the vertices of a rectangle.
Find the distance between the origin and the point:
(-5, -12)
The distance between the points (3, 1) and (0, x) is 5. Find x.
The centre of a circle is (2x - 1, 3x + 1). Find x if the circle passes through (-3, -1) and the length of its diameter is 20 unit.
The length of line PQ is 10 units and the co-ordinates of P are (2, -3); calculate the co-ordinates of point Q, if its abscissa is 10.
Calculate the distance between the points P (2, 2) and Q (5, 4) correct to three significant figures.
Find the distance of the following points from origin.
(5, 6)
Show that the points (2, 0), (–2, 0) and (0, 2) are vertices of a triangle. State the type of triangle with reason.
Seg OA is the radius of a circle with centre O. The coordinates of point A is (0, 2) then decide whether the point B(1, 2) is on the circle?

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:

The point on x axis equidistant from I and E is ______.
The point A(2, 7) lies on the perpendicular bisector of line segment joining the points P(6, 5) and Q(0, – 4).
