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

(4.8,3.8)

Step-by-step explanation:

We want to find the coordinates of the point that divides A(6, 1) and B(3, 8) in the ratio m:n=2:3

We use the section formula:

Let us substitute the points and the ratio to get:

This simplifies to:

The coordinates are (4.8,3.8)

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step-by-step explanation:

δabc ≅ δdcb by sas because

db ≅ ac . . given (side)

bc ≅ bc . . reflexive property (side)

∠dbc ≅ ∠ acb . . alternate interior angles where transversal bc crosses parallel lines bd and ac (included angle)