given the points A(-3,-4) and B(2,0), point P (-1,-12/5) partitions AB in the ratio A. 1:3 B. 2:1 C. 2:3 D. 3:2

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Question:

given the points A(-3,-4) and B(2,0), point P (-1,-12/5) partitions AB in the ratio A. 1:3 B. 2:1 C. 2:3 D. 3:2

Answer:

The point P (-1,-12/5) partitions the given line AB into two line segments with ratio: C. 2:3

How to divide lines into segments?

We are given the coordinates;

A(-3,-4) and B(2,0)

Now, P(-1,-12/5) partitions line AB

The point (-1, -12/5) lies on the line from A to B, but not in the center.

Thus, by using length of a line segment formula, we have;

AP = √[(-1 – (-3))² + (-12/5 – (-4))²] =

AP = √[2² + 1.6²] =

AP = √6.56

AP = 2.561

PB = √[(-1 – 2)² + (-12/5 – 0)²]

PB = √[(-3)² + (-12/5)²]

PB = √14.76

PB = 3.842

Thus;

AP:PB = 2.561 : 3.842  This is approximately a ratio of  2:3

Thus, the point P partitions AB into two line segments with ratio 2:3

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