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# Find the co-ordinates of the mid-point of the line segments joining the following pairs of points: (i) (2, – 3), ( – 6, 7) (ii) (5, – 11), (4, 3) (iii) (a + 3, 5b), (2a – 1, 3b + 4)

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ICSE Board Question Based on Section Formula Chapter of M.L Aggarwal for class10
In this question pairs of points are given to find the co-ordinates of the mid-point of the line segments joining this points.
This is the Question Number 01, Exercise 11 of M.L Aggarwal.

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1. Co-ordinates of midpoint of line joining the points (x1,y1) and (x2,y2) = {(x1+x2)/2 ,(y1+y2)/2}

(i) Co-ordinates of midpoint of line joining the points (2, -3) and (-6,7) = {(2+-6)/2, (-3+7)/2}

= (-4/2, 4/2)

= (-2, 2)

Hence the co-ordinates of midpoint of line joining the points (2, -3) and (-6,7) is (-2, 2).

(ii) Co-ordinates of midpoint of line joining the points (x1,y1) and (x2,y2) = {(x1+x2)/2 ,(y1+y2)/2}

Co-ordinates of midpoint of line joining the points (5, -11) and (4,3) = {(5+4)/2, (-11+3)/2}

= (9/2, -8/2)

= (9/2, -4)

Hence the co-ordinates of midpoint of line joining the points (5, -11) and (4,3) is (9/2, -4).

(iii) Co-ordinates of midpoint of line joining the points (x1,y1) and (x2,y2) = {(x1+x2)/2 ,(y1+y2)/2}

Co-ordinates of midpoint of line joining the points (a+3, 5b) and (2a-1,3b+4) = {(a+3+2a-1)/2, (5b+3b+4)/2}

= {(3a+2)/2, (8b+4)/2}

= {(3a+2)/2, (4b+2)}

Hence the co-ordinates of midpoint of line joining the points (a+3, 5b) and (2a-1,3b+4) are {(3a+2)/2, (4b+2)}.

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