FIND THE MIDPOINT OF THE LINE SEGMENT WHOSE ENDPOINTS ARE GIVEN

About "Find the Midpoint of the Line Segment Whose Endpoints are Given"

Find the Midpoint of the Line Segment Whose Endpoints are Given

Here we are going to see some example problems to find the midpoint of the line segment when endpoints are given.

The mid-point M of the line segment joining the points A(x₁, y₁) and B(x₂ , y₂) is

Find the Midpoint of the Line Segment Whose Endpoints are Given - Practice questions

Question 1 :

Find the mid-points of the line segment joining the points

(i) (−2, 3) and (−6,−5)

Solution :

(x₁, y₁) ==>  (-2, 3)

(x₂ , y₂) ==> (-6, -5)

Midpoint  =  (-2 - 6)/2, (3 + (-5))/2

   =  -8/2, -2/2

  =  (-4, -1)

(ii) (8,−2) and (−8,0)

Solution :

(x₁, y₁) ==>  (8, -2)

(x₂ , y₂) ==> (-8, 0)

Midpoint  =  (8 - 8)/2, (-2 + 0)/2

   =  0/2, -2/2

  =  (0, -1)

(iii) (a, b) and (a + 2b, 2a - b)

Solution :

(x₁, y₁) ==>  (a, b)

(x₂ , y₂) ==> (a + 2b, 2a - b)

Midpoint  =  (a + a + 2b)/2, (b + 2a - b)/2

   =  2(a + b)/2, 2a/2

  =  (a + b, 1)

(iv) (1/2, -3/7) and (3/2, -11/7)

Solution :

(x₁, y₁) ==>  (1/2, -3/7)

(x₂ , y₂) ==> (3/2, -11/7)

Midpoint  =  ((1/2) + (3/2))/2, ((-3/7) + (-11/7))/2

 =  ((4/2)/2, ((-14/7)/2)

=  (1, -1)

Question 2 :

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

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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