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Question
Find distance between point A(7, 5) and B(2, 5).
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Solution
Let A(x1, y1) = A(7, 5) and B(x2, y2) = B(2, 5)
∴ By distance formula,
d(A, B) = `sqrt((x_2 - x_1)^2 + (y_2 - y_1)^2`
= `sqrt((2 - 7)^2 + (5 - 5)^2`
= `sqrt((-5)^2 + 0^2)`
= `sqrt(25)`
= 5 cm
∴ The distance between points A and B is 5 cm.
RELATED QUESTIONS
Find the distance between two points
(i) P(–6, 7) and Q(–1, –5)
(ii) R(a + b, a – b) and S(a – b, –a – b)
(iii) `A(at_1^2,2at_1)" and " B(at_2^2,2at_2)`
Show that four points (0, – 1), (6, 7), (–2, 3) and (8, 3) are the vertices of a rectangle. Also, find its area
Check whether (5, -2), (6, 4) and (7, -2) are the vertices of an isosceles triangle.
Name the type of quadrilateral formed, if any, by the following point, and give reasons for your answer:
(−3, 5), (3, 1), (0, 3), (−1, −4)
ABC is a triangle and G(4, 3) is the centroid of the triangle. If A = (1, 3), B = (4, b) and C = (a, 1), find ‘a’ and ‘b’. Find the length of side BC.
An equilateral triangle has two vertices at the points (3, 4) and (−2, 3), find the coordinates of the third vertex.
A(–8, 0), B(0, 16) and C(0, 0) are the vertices of a triangle ABC. Point P lies on AB and Q lies on AC such that AP : PB = 3 : 5 and AQ : QC = 3 : 5. Show that : PQ = `3/8` BC.
Find the distance between the points:
A(9, 3) and B(15, 11)
Find all possible values of y for which the distance between the points A(2, –3) and B(10, y) is 10 units.
Find the distance between the following pair of point.
T(–3, 6), R(9, –10)
Find the distance between the following pairs of point in the coordinate plane :
(13 , 7) and (4 , -5)
Find the distance of the following point from the origin :
(13 , 0)
Prove that the points (a, b), (a + 3, b + 4), (a − 1, b + 7) and (a − 4, b + 3) are the vertices of a parallelogram.
Show that the points P (0, 5), Q (5, 10) and R (6, 3) are the vertices of an isosceles triangle.
Show that (-3, 2), (-5, -5), (2, -3) and (4, 4) are the vertices of a rhombus.
Find the distance of the following points from origin.
(5, 6)
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:
If a player P needs to be at equal distances from A and G, such that A, P and G are in straight line, then position of P will be given by ______.
Points A(4, 3), B(6, 4), C(5, –6) and D(–3, 5) are the vertices of a parallelogram.
Ayush starts walking from his house to office. Instead of going to the office directly, he goes to a bank first, from there to his daughter’s school and then reaches the office. What is the extra distance travelled by Ayush in reaching his office? (Assume that all distances covered are in straight lines). If the house is situated at (2, 4), bank at (5, 8), school at (13, 14) and office at (13, 26) and coordinates are in km.
Find the distance between the points O(0, 0) and P(3, 4).
