Question

A point M on a segment with endpoints X (1, −2) and Y (10, 3) partitions the segment in a 5:1 ratio. Find M. You must show all work to receive credit.

Answer 1

The point M is given by coordinates; (8.5, 2.16)

Ratio coordinate

The ratio XM : MY is 5:1

Therefore, on the x-axis;

The coordinate of M can be evaluated as follows;

• 5/1 = (a-1)/(10-a)

By Cross-product;

• 50 -5a = a -1

• 51 = 6a

• a = 8.5.

Similarly, on the y-axis;

The coordinate of M can be evaluated as follows;

• 5/1 = (b-(-2))/(3-b)

By Cross-product;

• 15 -5b = b +2

• 13 = 6b

• b = 2.16.

Ultimately, the coordinate of point M is; (8.5, 2.16)

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