Question

The endpoints of bar (DEF ) are D(1,4) and F(16,14). Determine and state the coordinates of point E, if DE:EF=2:3.

Answer 1

To find the coordinates of point E, which divides the line segment DF in the ratio 2:3, we apply the section formula to get E(7,8).

Step-by-step explanation:

To find the coordinates of point E, we need to apply the concept of section formula in coordinate geometry. Since the ratio of DE to EF is 2:3, point E divides segment DF internally in the ratio 2:3.

Step-by-step explanation:

1. First, let's write down the coordinates of points D and F, which are D(1,4) and F(16,14) respectively.
2. Now, using the section formula, which states that the coordinates of a point dividing a segment in the ratio m:n are given by: (mx2 + nx1) / (m + n), (my2 + ny1) / (m + n) where x1, y1 and x2, y2 are the coordinates of the endpoints of the segment.
3. Plug in the values: x1=1, y1=4, x2=16, y2=14, m=2 and n=3 into the formula:
   E's x-coordinate = (2*16 + 3*1) / (2+3) = (32 + 3) / 5 = 35 / 5 = 7
   E's y-coordinate = (2*14 + 3*4) / (2+3) = (28 + 12) / 5 = 40 / 5 = 8
4. Hence, point E has coordinates E(7,8).