Question

What are the coordinates of the point on the directed line segment from (-8, -10)(−8,−10) to (6, -6)(6,−6) that partitions the segment into a ratio of 3 to 1?

Answer 1

Answer:

(2.5, -7)

Step-by-step explanation:

Given:

Two end points of a line segment are given as:

(-8, -10) and (6, -6)

The ratio of partition is 3 : 1.

Let the line segment be AB with A(-8, -10) and B(6, -6). Let point P(x,y) divide the line segment AB in the ratio 3 : 1.

In order to find the point P, we use section formula which is given as:

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

Where, $(x_1,y_1)\ and\ (x_2,y_2)$ are end points of line segment AB divided in the ratio m : n by the point $(x, y)$.

Now, plug in the given values and solve for the coordinates of P. This gives,

$P(x,y)=(\frac{1\times -8+3\times 6}{3+1},\frac{1\times -10+3\times -6}{3+1})\\\\P(x,y)=(\frac{-8+18}{4},\frac{-10-18}{4})\\\\P(x,y)=(\frac{10}{4},\frac{-28}{4})\\\\P(x,y)=(2.5,-7)$

Therefore, the coordinates of the point on the directed line segment from (-8, -10) to (6,−6) that partitions the segment into a ratio of 3 to 1 is (2.5, -7).