Question

Which point is one fourth of the way between point A and point B on the line segment AB shown on the coordinate plane below?

Answer 1

The coordinate of the point between point A and point B on the line segment AB is $(\frac 92, -\frac{19}4)$

How to determine the point?

The points are given as:

A = (4,-5)

B = (6,-4)

m : n = 1 : 3

The coordinate of the point is then calculated using:

$P = \frac{1}{m + n}(mx_2 + nx_1,my_2 + ny_1)$

So, we have:

$P = \frac{1}{1 + 3}(1 * 6 + 3 * 4, 1 * -4 + 3 * -5)$

Evaluate the sum of product

$P = \frac{1}{4}(18, -19)$

Evaluate the product

$P = (\frac 92, -\frac{19}4)$

Hence, the coordinate of the point is $(\frac 92, -\frac{19}4)$

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