MIDPOINTOF THE LINE SEGMENT

Problem 1 :

The endpoints of RS are R(1, -3) and S(4, 2). Find the coordinates of the Midpoint M.

Solution :

Given, R(1, -3) and S(4, 2)

Midpoint M = [(x₁ + x₂)/2 , (y₁ + y₂)/2]

x₁ = 1,  y₁ = -3, x₂ = 4,  y₂ = 2

= (1 + 4)/2 , (-3 + 2)/2

= (5/2 , -1/2)

So, the coordinates of the Midpoint M = (5/2, -1/2)

Problem 2 :

The midpoint of JK is M(2, 1). One endpoint is J(1, 4). Find the coordinates of endpoint K.

Solution :

Coordinates of the Midpoint M = [(x₁ + x₂)/2 , (y₁ + y₂)/2]

Given, M(2, 1) and One endpoint is J(1, 4)

x₁ = 1,  y₁ = 4, x₂ = x₂,  y₂ = y₂

(2, 1) = [(1 + x₂)/2, (4 + y₂)/2]

Equating the x and y-coordinates, we get

So, the coordinates of endpoint K = (3, -2).

Problem 3 :

The endpoints of AB are A(1, 2) and B(7, 8). Find the coordinates of the midpoint M.

Solution :

Given, A(1, 2) and S(7, 8)

Coordinates of the Midpoint M = [(x₁ + x₂)/2 , (y₁ + y₂)/2]

x₁ = 1,  y₁ = 2, x₂ = 7,  y₂ = 8

= [(1 + 7)/2 , (2 + 8)/2]

= [8/2 , 10/2]

= [4, 5]

So, the coordinates of the midpoint M = [4, 5].

Problem 4 :

The midpoint of VW is M(-1, -2). One endpoint is W(4, 4). Find the coordinates of endpoint V.

Solution :

Coordinates of the Midpoint M = [(x₁ + x₂)/2 , (y₁ + y₂)/2]

Given, M(-1, -2) and One endpoint is W(4, 4)

x₁ = 4,  y₁ = 4, x₂ = x₂,  y₂ = y₂

(-1, -2) = [(4 + x₂)/2, (4 + y₂)/2]

Equating the x and y-coordinates, we get

So, the coordinates of endpoint K = (-6, -8).

Find the coordinates of the midpoint of the segment with the given endpoints.

Problem 5 :

C(3, 5) and D(7, 5)

Solution :

Given, C(3, 5) and D(7, 5)

Coordinates of the Midpoint M = [(x₁ + x₂)/2 , (y₁ + y₂)/2]

x₁ = 3,  y₁ = 5, x₂ = 7,  y₂ = 5

= [(3 + 7)/2 , (5 + 5)/2]

= (10/2 , 10/2)

= (5, 5)

So, the coordinates of the Midpoint is (5, 5).

Problem 6 :

E(0, 4) and F(4, 3)

Solution :

Given, E(0, 4) and F(4, 3)

Coordinates of the Midpoint M = [(x₁ + x₂)/2 , (y₁ + y₂)/2]

x₁ = 0,  y₁ = 4, x₂ = 4,  y₂ = 3

= (0 + 4)/2 , (4 + 3)/2

= (4/2 , 7/2)

= (2, 7/2)

So, the coordinates of the Midpoint M = (2, 7/2)

Problem 7 :

G(-4, 4) and H(6, 4)

Solution :

Given, G(-4, 4) and H(6, 4)

Coordinates of the Midpoint M = [(x₁ + x₂)/2 , (y₁ + y₂)/2]

x₁ = -4,  y₁ = 4, x₂ = 6,  y₂ = 4

= [(-4 + 6)/2 , (4 + 4)/2]

= [2/2 , 8/2]

= [1, 4]

So, the coordinates of the Midpoint M = [1, 4].

Problem 8 :

J(-7, -5) and K(-3, 7)

Solution :

Given, J(-7, -5) and K(-3, 7)

Coordinates of the Midpoint M = [(x₁ + x₂)/2 , (y₁ + y₂)/2]

x₁ = -7,  y₁ = -5, x₂ = -3,  y₂ = 7

= [(-7 - 3)/2 , (-5 + 7)/2]

= [-10/2 , 2/2]

= [-5, 1]

So, the coordinates of the Midpoint M = [-5, 1].

Problem 9 :

P(-8, -7) and Q(11, 5)

Solution :

Given, P(-8, -7) and Q(11, 5)

Coordinates of the Midpoint M = [(x₁ + x₂)/2 , (y₁ + y₂)/2]

x₁ = -8,  y₁ = -7, x₂ = 11,  y₂ = 5

= [(-8 + 11)/2 , (-7 + 5)/2]

= [3/2 , -2/2]

= [1.5, -1]

So, the coordinates of the Midpoint M = [1.5, -1].

Problem 10 :

S(-3, 3) and T(-8, 6)

Solution :

Given, S(-3, 3) and T(-8, 6)

Coordinates of the Midpoint M = [(x₁ + x₂)/2 , (y₁ + y₂)/2]

x₁ = -3,  y₁ = 3, x₂ = -8,  y₂ = 6

= (-3 - 8)/2 , (3 + 6)/2

= (-11/2 , 9/2)

So, the coordinates of the Midpoint M = (-11/2 , 9/2).