Question

The line segment joining A(6, 3) to B(–1, –4) is doubled in length by having half its length added to each end. Find the coordinates of the new ends.

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Answer 1

• (9.5, 6.5) and (-4.5, -7.5)

Explanation:

Let the extended points be A' and B' and add the point M as midpoint of AB

Coordinates of M are:

• ((6 - 1)/2, (3-4)/2) = (2.5, -0.5)

Now point A is midpoint of A'M and point B is midpoint of MB'

Finding the coordinates using midpoint formula:

• A' = ((2*6 - 2.5),(2*3 - (-0.5)) = (9.5, 6.5)
• B' = ((2*(-1) - 2.5), (2*(-4) - (-0.5)) = (-4.5, -7.5)