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.

Practice Questions

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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