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If point C is at -9 and point D is at 7, find a point E on CD such that the ratio of CE to is CD is 3/4. The answer should be -7, 3, 12, or 5.

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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).

User Remorath
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