Question

Can someone please explain the equation I am supposed to use ​

Answer 1

9514 1404 393

Answer:

• M
• L
• N
• 1 : 3

Explanation:

There are several ways you can go at this. Perhaps the most complicated is using the distance formula to determine the various ratios. Since all of the points are on the same line segment, I find it easier just to consider the x-coordinate differences. (The length of PQ is Q - P for the purposes here.)

For x-coordinates only, ...

L -A = -1 -(-3) = 2

M -A = 0 -(-3) = 3

N -A = 1 -(-3) = 4

Z -A = 3 -(-3) = 6

Note that the corresponding distances from Z are ...

Z -L = 3 -(-1) = 4

Z -M = 3 -0 = 3

Z -N = 3 -1 = 2

Then the ratios are ...

AL : LZ = 2 : 4 = 1 : 2 . . . . . partitioning by point L

AM : MZ = 3 : 3 = 1 : 1 . . . . partitioning by point M

AN : NZ = 4 : 2 = 2 : 1 . . . . partitioning by point N

AL : AZ = 2 : 6 = 1 : 3 . . . . partitioning by L expressed differently

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Now we have what we need to answer the questions.

Point M partitions into 1 : 1

Point L partitions into 1 : 2

Point N partitions into 2 : 1

AL : AZ = 1 : 3