Question

PLEASE HELP ME!!!! 50 points!

Given the points C(-1, -3) and D(5, 6), find the coordinates of the point E on directed line segment CD that partitions CD into the ratio 2 to 1.

A. (1, 0)

B. (3, 3)

C. (-3, 3)

D. (2, 1.5)

Answer 1

b

Explanation:

bc yes

Answer 2

B. (3,3)

Explanation:

In order to find the coordinates of point E that partitions the line segment CD into a ratio of 2:1, we can use the following formula for finding the coordinates of a point that divides a line segment in a given ratio:

For a line segment with endpoints A(x1, y1) and B(x2, y2), and a division ratio of m:n, the coordinates of the point E(x, y) that divides the line segment in this ratio are given by:

`\sf x =( (m* x_2 + n* x_1) )/((m + n))`

`\sf y =( (m* y_2 + n* y_1) )/((m + n))`

In this case, we want to divide the line segment CD into a ratio of 2:1, so m = 2 and n = 1.

Wehave the coordinates of C(-1, -3) and D(5, 6).

Using the formula:

`\begin{aligned} x &\sf =( (2* 5 + 1* (-1)))/( (2 + 1)) \\\\ &\sf = (10-1)/(3)\\\\ &\sf = (9)/(3)\\\\ &\sf = 3 \end{aligned}`

and

`\begin{aligned} y &\sf =( (2* 6 + 1* (-3)) )/( (2 + 1)) \\\\ &\sf = (12-3)/(3) \\\\ &\sf = (9)/(3)\\\\ &\sf = 3 \end{aligned}`

So, the coordinates of point E that partitions the line segment CD into a ratio of 2:1 are E(3, 3).

So, the answer is B. (3,3)