How to Find the Missing Coordinates if Three Points Lie on the Line

HOW TO FIND THE MISSING COORDINATES IF THREE POINTS LIE ON THE LINE

Here we are going to see, how to find the missing coordinates if three points lie on the same line.

Slope :

If (x₁,y₁) and (x_2,y₂) are any two points on a line, with x₁≠x2, then the slope of the line is

(y₂ − y₁) / (x₂ − x₁)

We will get the same slope for any two points lie on the same line.

Question 1 :

Find a number t such that the point (−2, t) is on the line containing the points (5,−2) and (10,−8).

Answer :

Slope of the line passing through the points (-2, t) and (5, -2) = Slope of the line passing through the points (5, -2) and (10, -8).

Slope m = (y₂ - y₁)/ (x₂ - x₁)

(x₁, y₁) ==> (-2, t) and (x₂, y₂) ==> (5, -2)

m = (-2 - t)/(5 + 2)

m = (-2 - t)/7 ----(1)

(x₁, y₁) ==> (5, -2) and (x₂, y₂) ==> (10, -8)

m = (-8 + 2)/(10 - 5)

m = -6/5 ----(2)

-(2 + t)/7 = -6/5

5(2 + t) = 42

10 + 5t = 42

5t = 42 - 10

5t = 32

t = 32/5

Question 2 :

Find a number t such that the point (t, 2t) is on the line containing the points (3,−7) and (5,−15).

Answer :

Slope m = (y₂ - y₁)/ (x₂ - x₁)

(x₁, y₁) ==> (t, 2t) and (x₂, y₂) ==> (3, -7)

m = (-7 - 2t)/(3 - t) ---(1)

(x₁, y₁) ==> (3, -7) and (x₂, y₂) ==> (5, -15)

m = (-15 + 7)/(5 - 3)

m = -8/2

m = -4----(2)

(-7 - 2t)/(3 - t) = 4

-7 - 2t = 4(3 - t)

-7 - 2t = 6 - 4t

-2t + 4t = 6 + 7

2t = 13

t = 13/2

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