The centre of a circle is (−4,2). If one end of the diameter of the circle is (−3,7), then find the other end

Solution :

Midpoint of the diameter = Center of the circle

Let the other endpoint be (a, b)

Midpoint of (-3, 7) and (a, b) is (-4, 2).

(-3 + a)/2, (7 + b)/2 = (-4, 2)

By equating the x and y coordinates, we get

(-3 + a)/2 = -4

-3 + a = -8

a = -8 + 3

a = -5

(7 + b)/2 = 2

7 + b = 4

b = 4 - 7

b = -3

Hence the other end is (-5, -3).

Question 3 :

If the mid-point (x, y) of the line joining (3, 4) and (p, 7) lies on 2x + 2y + 1 = 0 , then what will be the value of p?

Solution :

Midpoint of the line segment joining the points (3, 4) and (p, 7)

(3 + p)/2 , (7 + 4)/2 = (x, y)

(3 + p)/2 , 11/2 = (x, y)

x = (3 + p)/2 and y = 11/2

Since the midpoint lies on the line 2x + 2y + 1 = 0

2(3 + p)/2 + 2(11/2) + 1 = 0

3 + p + 11 + 1 = 0

p + 15 = 0

p = -15

After having gone through the stuff given above, we hope that the students would have understood, "Find the Midpoint of the Line Segment Whose Endpoints are Given"

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