Question

answer step by step please​

Answer 1

Step-by-step explanation:

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

Case I: Points X, Y, Z are such that, X – Y – Z.

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

∴ d(X, Z) = 25 Case II: Points X, Y, Z are such that, X – Z – Y.

∴ d(X,Y) = d(X,Z) + d(Z,Y)

∴ 17 = d(X, Z) + 8

∴ d(X, Z) = 17 – 8

∴ d(X, Z) = 9 Case III: Points X, Y, Z are such that, Z – X – Y.

From the diagram, d(X, Y) > d (Y, Z)

Which is not possible

∴ Point X is not between Z and Y.

∴ d(X, Z) = 25 or d(X, Z) = 9.

Answer 2

Answer:

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

d(X,Z) = 25 or 9

Step-by-step explanation:

d(X,Y)=17,

d(Y,Z)=8

now if Z is not in between X & Y

then

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

=> d(X,Z) = 17 + 8 = 25

now if Z is in between X & Y

then

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

=> d(X,Z) = 17 - 8 = 9

$.$