On a coordinate plane, a line is drawn from point A to point B. Point A is at (negative 4, 8) and point B is at (2, negative 4).

Question

2 years ago

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On a coordinate plane, a line is drawn from point A to point B. Point A is at (negative 4, 8) and point B is at (2, negative 4).

What are the x- and y-coordinates of point C, which partitions the directed line segment from A to B into the ratio 3:10? Round to the nearest tenth, if necessary. X = y =.

Mathematics

2 answers:

antiseptic1488 [7] · Answer 1 · 2023-03-29T05:51:58+03:00

The x and y coordinates of point C are -2.6 and 5.2, respectively

The coordinate of the points are given as:

$A = (-4,8)$

$B =(2,-4)$

The ratio is given as:

$m :n = 3 : 10$

The point at the given ratio is calculated as:

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

So, we have:

$C = (\frac{3 \times 2 + 10 \times -4}{3+10},\frac{3 \times -4 +10 \times 8}{3+10})$

Simplify

$C = (\frac{-34}{13},\frac{68}{13})$

$C = (-2.6,5.2)$

Hence, the x and y coordinates of point C are -2.6 and 5.2, respectively