I have no clue to this. Please help. Line segment CD has endpoints with coordinates (1,2) and (9,6). What is the location for point E so that E divides CD into the ratio 3:1?
You want E to be 3/4 of the way from C to D.
So, for both x and y, you want to go 3/4 of the distance from C to D.
The x-coordinates differ by 8
The y-coordinates differ by 4
So, you want to add (6,3) to C, making E=(1,2)+(6,3)=(7,5)
To find the location of point E that divides the line segment CD into a ratio of 3:1, we can use the concept of the section formula.
The section formula states that if a line segment has endpoints (x1, y1) and (x2, y2) and is divided by a point E in the ratio of m:n, then the coordinates of E can be found using the formula:
Ex = (nx2 + mx1) / (m + n)
Ey = (ny2 + my1) / (m + n)
In this case, the endpoints of line segment CD are (1,2) and (9,6), and we want to divide it into a ratio of 3:1.
Using the section formula, we can calculate the coordinates of point E.
Substituting the values into the formula:
Ex = (1 * 9 + 3 * 1) / (3 + 1)
= (9 + 3) / 4
= 12 / 4
= 3
Ey = (1 * 6 + 3 * 2) / (3 + 1)
= (6 + 6) / 4
= 12 / 4
= 3
Therefore, the coordinates of point E are (3,3).