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Question: 1. Line segment AB has endpoints A(8, 3) and B(2, 6). Find the coordinates of the point that divides the line segment directed from A to B in the ratio of 1:2. 2. Line segment AB has endpoints A(6, 4) and B(2, 6). Find the coordinates of the point that divides the line segment directed from A to B in the ratio of 1:3.

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Ahayes1111idn

Answer:

a) (6,4)

b) (5, 4.5)

Step-by-step explanation:

much like when you find them midpoint where you average the x-coordinates and the y-coordinates to find the midpoint coordinates, you'll do the same thing here.

to set context, a midpoint would break the segment into a ratio of 1:1.

so in the first part, a ratio of 1:2 means you are breaking the segment into 3-parts. So you'll do this for the coordinates:

[tex]x = \frac{8 + 2}{3} \: and \: y = \frac{3 + 6}{3} [/tex]

for the second part as the ratio is 1:3, you are breaking the segment into 4 parts.

[tex]x = \frac{6 + 2}{4} \: and \: y = \frac{4 + 6}{4} [/tex]

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