Q. 53.7( 20 Votes )

# Points X, Y, Z are collinear such that d (X, Y) = 17, d (Y, Z) = 8 find d(X, Z).

Answer :

Given: X, Y and Z are collinear and

d (X, Y) = 17, d (Y, Z) = 8

We know that

If X, Y and Z are three distinct collinear points, then there are three possibilities:

(i) Point Y is between X and Z

(ii) Point Z is between X and Y

(iii) Point X is between Y and Z

Now, let (i) holds true, i.e. Point Y is between X and Z, then

d (X, Y) + d (Y, Z) = d (X, Z)

⇒ d (X, Z) = 17 + 8 = 25

⇒ d (X, Z) = 25

Next, let (ii) holds true, i.e. Point Z is between X and Y, then

d (X, Z) + d (Y, Z) = d (X, Y)

⇒ d (X, Z) = d (X, Y) - d (Y, Z) = 17 – 8 = 9

⇒ d (X, Z) = 9

Lastly, let (iii) holds true, i.e. Point X is between Y and Z, then

d (X, Y) + d (X, Z) = d (Y, Z)

⇒ d (X, Z) = d (Y, Z) – d (X, Y) = 8 – 17 = -9

⇒ d (X, Z) = -9, which is not possible as distance between any two points is a non-negative real number.

Hence, the value of d (X, Z) is either 25 or 9.

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Find the distances with the help of the number line given below.

i. d(B, E)

ii. d(j, A)

iii. d(P, C)

iv. d(J, H)

v. d(K, O)

vi. d(O, E)

vii. d(Q, B)

MHB - Math Part-IIWhich figure is formed by three non-collinear points?

MHB - Math Part-II