A -Find the equation of the straight line joining the points (1, 2) and (5, 4)

Question

B - Find the midpoint of the line joining (1, 2) and (5,4)?

Answer 1

A).

Slope - intercept form of the line equation is y = mx + b, where m is slope and b is y - intercept.

 

Let the points are (x₁, y₁) = (1, 2) and (x₂, y₂) = (5, 4).

Slope (m) = [(y₂ - y₁)/(x₂ -x₁)]

m = [(4 - 2)/(5 - 1)]

m  = [2/4]

⇒ m = 1/2.

Now, the line equation is y = (1/2)x + b.

 

Find the y - intercept by substituting any point in the line equation say (x, y) = (1, 2).

2 = (1/2)(1) + b

b = 2 - 1/2

b = (4 - 1)/2

⇒ b = 3/2.

The line equation is y = (1/2)x + (3/2).

Answer 2

B).

Let the points are A(x₁, y₁) = (1, 2) and B(x₂, y₂) = (5, 4).

Mid point of the line joining A and B : M = [ (x₁+ x₂)/2 , (y₁+ y₂)/2].

= [ (1+ 5)/2 , (2+ 4)/2]

= [ 6/2 , 6/2]

= [ 3 , 3].

Therefore, the mid point of the line joining (1, 2) and (5, 4) is (3, 3).