# FIND MISSING COORDINATE USING DISTANCE FORMULA

## About "Find missing coordinate using distance formula"

Find missing coordinate using distance formula :

Here we are going to see some examples to find missing coordinate using distance formula.

Example 1 :

Find the value of a if the distance between the points at (7, 5) and (a, -3) is 10 units.

Solution :

d = (x2 - x1)2 + (x2 - x1)2

Let x2 = a, x1 = 7, y2 = -3, y1 = 5

Here d  =  10

10 = (a - 7)2 + (-3-5)2

10 = (a - 7)2 + (-8)2

10 = (a - 7)2 + 64

10 (a2 - 2 a (7) + 72) + 64

10 (a2 - 14 a + 113)

Taking squares on both sides

102 = ((a2 - 14 a + 113)2

a2 - 14 a + 113 - 100  =  0

a2 - 14 a + 13  =  0

(a - 1) (a - 13)  =  0

a  =  1  (or)  a  =  13

Hence the missing coordinates are 1 or 13.

Example 2 :

Find the value of a if the distance between the points at (3, -1) and (a, 7) is 10 units.

Solution :

d = (x2 - x1)2 + (x2 - x1)2

Let x2 = a, x1 = 3, y2 = 7, y1 = -1

Here d  =  10

10 = (a - 3)2 + (7 - (-1))2

10 = (a - 3)2 + (7 + 1)2

10 = (a - 3)2 + (8)2

10 (a2 - 2 a (3) + 32) + 64

10 (a2 - 6a + 9 + 64)

10 (a2 - 6a + 73)

Taking squares on both sides

102 = ((a2 - 6 a + 73)2

a2 - 6 a + 73 - 100  =  0

a2 - 6 a - 27  =  0

(a - 9) (a + 3)  =  0

a  =  9  (or)  a  =  -3

Hence the missing coordinates are 9 or -3.

Example 3 :

Find the value of a if the distance between the points at (10, a) and (1, -6) is 145 units.

Solution :

d = (x2 - x1)2 + (x2 - x1)2

Let x2 = 1, x1 = 10, y2 = -6, y1 = a

Here d  =  145

145 = (1 - 10)2 + (-6 - a)2

145 = (- 9)2 + (-6 - a)2

145 = √81 + (6 + a)2

145 = √81 + (62 + 2(6) a + a2)

145 = √(81 + 36 + 12 a + a2)

145 = a2 + 12a + 117

Taking squares on both sides

(√145)2 = (a2 + 12a + 117)2

a2 + 12 a + 117 - 145  =  0

a2 + 12 a - 28  =  0

(a + 14) (a - 2)  =  0

a  =  -14  (or)  a  =  2

Hence the missing coordinates are -14 or 2.

After having gone through the stuff given above, we hope that the students would have understood "Find missing coordinate using distance formula".

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