Answer:
To find a point E on the line segment CD such that the ratio of CE to CD is 3/4, we can use the concept of linear interpolation. Linear interpolation is a method used to estimate an unknown value between two known values based on their relative positions.
Given that point C is at -9 and point D is at 7, we can calculate the length of CD by subtracting the x-coordinates of C and D:
CD = D - C = 7 - (-9) = 16
Now, let's assume that point E lies on the line segment CD. We can express the position of E in terms of its distance from C as a fraction of the total length CD. Let's call this fraction t.
CE = t * CD
According to the given information, the ratio of CE to CD is 3/4. Therefore, we can write:
CE / CD = 3/4
Substituting the expressions for CE and CD:
(t * CD) / CD = 3/4
Simplifying:
t = 3/4
This means that point E is located at a distance of (3/4) * CD from point C.
Substituting the value of CD:
t = (3/4) * 16
t = 12
Therefore, point E is located at a distance of 12 units from point C.
To determine the coordinates of point E, we need to consider the direction in which we move from point C towards point D. Since D has a greater x-coordinate than C, we move in the positive x-direction.
Starting from point C (-9), we move 12 units in the positive x-direction:
E_x = C_x + t
E_x = -9 + 12
E_x = 3
Thus, the x-coordinate of point E is 3.
Since E lies on the line segment CD, its y-coordinate will be the same as that of point C.
E_y = C_y
E_y = 0
Therefore, the coordinates of point E are (3, 0).
In summary, the point E on the line segment CD, such that the ratio of CE to CD is 3/4, is located at (3, 0).