Question

M is the midpoint of AB and C is the midpoint of AM. Let the coordinate of A=7y and the coordinate of B=3x. Find the coordinate of C in terms of x and y.

Answer 1

Given :-

• M is the midpoint of AB .
• C is the midpoint of AM.
• The coordinate of A = 7y.
• The coordinate of B = 3x.

To Find :-

• The coordinate of C in terms of x and y. ?

Formula used :-

• The coordinate of the mid - point of a line is given by adding the values of the two end points and then dividing the result by 2. { or Average of Both end Points.}

Solution :-

→ coordinate of A = 7y .

→ coordinate of B = 3x .

→ M is the Mid Point of AB.

So,

→ coordinate of M = Average of A and B

→ coordinate of M = (A + B)/2

→ coordinate of M = (7y + 3x)/2 .

Now, we have given that, C is the midpoint of AM.

Therefore,

→ The coordinate of point C = Average of A and M .

→ C coordinate = (A + M) / 2

→ C coordinate = [ 7y + {(7y + 3x)/2} ] / 2

→ C coordinate = (14y + 7y + 3x) / (2 * 2)

→ C coordinate = (21y + 3x) / 4

→ C coordinate = (3/4)(7y + x) (Ans.)

Hence, The coordinate of C is (3/4)(7y + x) .