HOW TO FIND THE MISSING COORDINATE USING SLOPE

How to Find the Missing Coordinate Using Slope ?

Here we are going to see, how to find the missing coordinate using slope.

If the given points are collinear, then their slopes will be equal.

By suing this concept, we may find the missing coordinate. Let us look into some problems based on this concept.

How to Find the Missing Coordinate Using Slope - Questions

Question 1 :

Show that the given points are collinear: (-3,-4) , (7,2) and (12,5)

Solution :

Let A (-3, -4) B (7, 2) and C (12, 5) the given points.

Slope of AB  =  (y2 - y1)/(x2 - x1)

   =  [2 - (-4)]/[7 - (-3)]

   = (2 + 4)/(7 + 3)

   = 6/10

  =  3/5

Slope of BC  =  (y2 - y1)/(x2 - x1)

   =  (5 - 2)/(12 - 7)

   =  3/5

Hence the given points are collinear.

Question 2 :

If the three points (3,-1) , (a, 3) and (1,-3) are collinear, find the value of a.

Solution :

Let the given points be A (3,-1) B (a, 3) and C (1,-3)

Slope of AB  =  (y2 - y1)/(x2 - x1)

  =  (3-(-1))/(a - 3)

  =  (3 + 1)/(a - 3)

  =  4/(a-3)  ----(1)

Slope of BC  =  (y2 - y1)/(x2 - x1)

  =  (-3-3)/(1 - a)

  =  -6/(1 - a) ----(2)

(1)  =  (2)

4/(a - 3)  =  -6/(1 - a)

4(1 - a)  =  -6(a - 3)

4 - 4a  =  -6a + 18

6a - 4a  =  18 - 4

2a  =  14

a  =  7

Hence the value of a is 7.

Question 3 :

The line through the points (-2, a) and (9, 3) has slope -1/2. Find the value of a.

Solution :

Slope of the line passing through the given points  =  -1/2

(-2, a) (9, 3)

m   (y2 - y1)/(x2 - x1)

m  =  (3 - a)/(9 - (-2))

   (3 - a)/(9 + 2)  =  -1/2

   (3 - a)/11  =  -1/2

2(3 - a)  =  -11

6 - 2a  =  -11

-2a  =  -11 -6

a  =  17/2

Hence the value of a is 17/2.

Question 4 :

The line through the points (-2,6) and (4,8) is perpendicular to the line through the points (8,12) and (x,24) . Find the value of x.

Solution :

Slope of the line passing through the points (-2, 6) and (4, 8).

m  =  (8 - 6)/(4 - (-2))

  =  2/(4+2) 

  =  2/6

  =  1/3 -----(1)

Slope of the line passing through the points (8, 12) and (x, 24) .

m  =  (24 - 12)/(x - 8)

  =  12/(x - 8) -----(2)

Since these lines are perpendicular to each other,

(1/3) ⋅ 12/(x - 8) =  -1

4/(x - 8)  =  -1

4  =  -(x - 8)

4  =  -x + 8

x  =  8 - 4

x  =  4

After having gone through the stuff given above, we hope that the students would have understood, "How to Find the Missing Coordinate Using Slope". 

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