Question

Find the coordinates of point Q that lies along the directed line segment from R(-2, 4) to S(18, -6) and partitions the segment in the ratio of 3:7.

Answer 1

Answer:

The coordinates of the point Q is (4, 1)

Step-by-step explanation:

The given parameters are;

The directed line segment  extends from R(-2, 4), to S(18, -6)

The ratio in which the point Q partitions the directed line segment = 3:7

Therefore, the proportions of the R to Q = 3/(3 + 7) = 3/10 the length of RS

Which gives;

(-2 + (18-(-2))×3/10,  4 +(-6 -4)×3/10) which is (4, 1)

The coordinates of the point Q = (4, 1)

We check the length from R to S is given by the relation for length as follows

$l =\sqrt{\left (y_{2}-y_{1} \right )^{2}+\left (x_{2}-x_{1} \right )^{2}}$

Where;

R(-2, 4) = (x₁, y₁)

S(18, -6) = (x₂, y₂)

Length of segment RS  = 22.36

length from R to Q = 6.7086

We check RQ/RS = 6.7082/22.36 = 0.3

Also QS/RS = (22.36 - 6.7082)/22.36 = 0.6999≈ 0.7

The coordinates of the point Q = (4, 1).