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If [tex]L P = 15[/tex] and [tex]P R = 9[/tex], find [tex]L R[/tex]. Explain.

A. [tex]L R = 6[/tex] because [tex]L R + L P = P R[/tex] according to the Segment Addition Postulate, and [tex]6 + 9 = 15[/tex] using substitution.

B. [tex]L R = 24[/tex] because [tex]15 + 9 = 24[/tex] according to the addition property of equality.

C. [tex]L R = 24[/tex] because [tex]L P + P R = L R[/tex] according to the Segment Addition Postulate, and [tex]15 + 9 = 24[/tex] using substitution.

D. [tex]L R = 6[/tex] because [tex]15 - 9 = 6[/tex] according to the subtraction property of equality.



Answer :

GinnyAnswer
To find [tex]\(LR\)[/tex], given [tex]\(LP = 15\)[/tex] and [tex]\(PR = 9\)[/tex], we can use the Segment Addition Postulate. The Segment Addition Postulate states that if a point [tex]\(P\)[/tex] lies on a line segment [tex]\(LR\)[/tex], then the length of [tex]\(LR\)[/tex] is the sum of the lengths of [tex]\(LP\)[/tex] and [tex]\(PR\)[/tex].

In other words,

[tex]\[ LR = LP + PR \][/tex]

Let's substitute the given values into the equation:

[tex]\[ LP = 15 \][/tex]
[tex]\[ PR = 9 \][/tex]

Now, applying the Segment Addition Postulate, we get:

[tex]\[ LR = LP + PR \][/tex]
[tex]\[ LR = 15 + 9 \][/tex]

Adding these together:

[tex]\[ LR = 24 \][/tex]

So, the correct answer is [tex]\(LR = 24\)[/tex] because [tex]\(LP + PR = LR\)[/tex] according to the Segment Addition Postulate, and [tex]\(15 + 9 = 24\)[/tex] using substitution.

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