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5. Answer the following questions.

(i) If [tex]A - B - C[/tex] and [tex]d(A, C) = 17[/tex], [tex]d(B, C) = 6.5[/tex], then [tex]d(A, B) =[/tex]

(ii) If [tex]P - Q - R[/tex] and [tex]d(P, Q) = 3.4[/tex], [tex]d(Q, R) = 5.7[/tex], then [tex]d(P, R) =[/tex]

Sagot :

GinnyAnsweridn
Certainly! Let's solve these two parts step-by-step.

### Part (i)
Given:
- Points are in a straight line: [tex]\( A - B - C \)[/tex]
- Distance between [tex]\( A \)[/tex] and [tex]\( C \)[/tex], [tex]\( d(A, C) = 17 \)[/tex]
- Distance between [tex]\( B \)[/tex] and [tex]\( C \)[/tex], [tex]\( d(B, C) = 6.5 \)[/tex]

We need to find the distance between [tex]\( A \)[/tex] and [tex]\( B \)[/tex], [tex]\( d(A, B) \)[/tex].

Since point [tex]\( B \)[/tex] is between [tex]\( A \)[/tex] and [tex]\( C \)[/tex] on the straight line, we can use the relationship:
[tex]\[ d(A, C) = d(A, B) + d(B, C) \][/tex]

Given:
[tex]\[ 17 = d(A, B) + 6.5 \][/tex]

To find [tex]\( d(A, B) \)[/tex], we subtract [tex]\( d(B, C) \)[/tex] from [tex]\( d(A, C) \)[/tex]:
[tex]\[ d(A, B) = 17 - 6.5 \][/tex]

[tex]\[ d(A, B) = 10.5 \][/tex]

So, the distance between [tex]\( A \)[/tex] and [tex]\( B \)[/tex] is [tex]\( 10.5 \)[/tex].

### Part (ii)
Given:
- Points are in a straight line: [tex]\( P - Q - R \)[/tex]
- Distance between [tex]\( P \)[/tex] and [tex]\( Q \)[/tex], [tex]\( d(P, Q) = 3.4 \)[/tex]
- Distance between [tex]\( Q \)[/tex] and [tex]\( R \)[/tex], [tex]\( d(Q, R) = 5.7 \)[/tex]

We need to find the distance between [tex]\( P \)[/tex] and [tex]\( R \)[/tex], [tex]\( d(P, R) \)[/tex].

Since point [tex]\( Q \)[/tex] is between [tex]\( P \)[/tex] and [tex]\( R \)[/tex] on the straight line, we can use the relationship:
[tex]\[ d(P, R) = d(P, Q) + d(Q, R) \][/tex]

Given:
[tex]\[ d(P, R) = 3.4 + 5.7 \][/tex]

[tex]\[ d(P, R) = 9.1 \][/tex]

So, the distance between [tex]\( P \)[/tex] and [tex]\( R \)[/tex] is [tex]\( 9.1 \)[/tex].

### Summary:
(i) [tex]\( d(A, B) = 10.5 \)[/tex]
(ii) [tex]\( d(P, R) = 9.1 \)[/tex]
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