To get clear concept on how to find the mid-points between two given co-ordinate points student’s can practice the questions given in the worksheet on finding mid-point.
We know that the average distance between the two given points is known as the midpoint. Midpoint can be represented by any letter, for example M, N, O, P etc,.
Let us recall the formula for finding the midpoint between any two given points as follows;
Suppose, (x₁, y₁) and (x₂, y₂) be the co-ordinates of the points P and Q respectively and R, the mid-point of the line segment PQ. Then, the co-ordinates of R are ((x₁ + x₂)/2, (y₁ + y₂)/2).
To learn more about the formula for finding mid-point Click Here.
Find the co-ordinates of the mid-points of the line-segments joining each of the following pair of points :
(i) (3, 5) and (- 1, - 7)
(ii) (7, - 8) and (-3, 4)
(iii) (a, - b) and (- a, b)
(iv) (l, m) and (l + m, l - m).
2. (i) One extremity of a line-segment is the point (3, - 2) and the middle point of the line-segment is the point (- 2, 3). Find the co-ordinates of the other extremity.
(ii) A diameter of a circle has the extreme points (7, 9) and (- 1, - 3). What would be the co-ordinates of the centre ?
(iii) AB is' a diameter of a circle having centre at C; if the co-ordinates of A and C are (6, - 7) and (5, - 2), find the co-ordinates of B.
Answers for the worksheet on finding mid-point between two given points are given below to check the exact answers of the above questions on mid-point.
1. (i) (1, – 1)
(ii) (2, - 2)
(iii) (0, 0)
(iv) (l + m/2, l/2)
2. (i) (- 7, 8)
(ii) (3, 3)
(iii) (4, 3).
● Co-ordinate Geometry