Question

The endpoints of EF¯¯¯¯¯ are located at E (−3, 2) and F (3, 8). Point D divides EF¯¯¯¯¯ such that ED : DF is equal to 1 : 3. For each box, select the values in the dropdown that make the statement true. The x-coordinate of point D is and the y-coordinate of point D is

Answer 1

Answer:

$D(x,y) = (-1.5,3.5)$

Step-by-step explanation:

Given

$E = (-3,2)$

$F = (3,8)$

$ED: DF = 1 : 3$

Required

Determine the coordinates of D

This is calculated as thus:

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

Where:

$(x_1,y_1) = (-3,2)$

$(x_2,y_2) = (3,8)$

$m:n = 1:3$

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

$D(x,y) = (\frac{1 * 3 + 3 *-3}{1+3},\frac{1 * 8 + 3 * 2}{1+3})$

$D(x,y) = (\frac{-6}{4},\frac{14}{4})$

$D(x,y) = (-1.5,3.5)$