If point C is at -9 and point D is at 7, find a point E on CD¯¯¯¯¯¯¯¯

Question

such that the ratio of CE¯¯¯¯¯¯¯¯ to CD¯¯¯¯¯¯¯¯ is 3/4

Answer 1

First, let's find the length of CD¯¯¯¯¯¯¯¯. The distance between -9 and 7 is 7 - (-9) = 16.

Let x be the length of CE¯¯¯¯¯¯¯¯. Since the ratio of CE¯¯¯¯¯¯¯¯ to CD¯¯¯¯¯¯¯¯ is 3/4, we can set up the following equation:

x / 16 = 3/4

To solve for x, we can cross-multiply:

4x = 3 * 16

4x = 48

x = 48/4

x = 12

Therefore, the length of CE¯¯¯¯¯¯¯¯ is 12.

To find the coordinates of point E, we subtract 12 from the x-coordinate of D. Since D is at 7, E will be at:

7 - 12 = -5

So the coordinates of point E are (-5, -9).

Answer 2

The midpoint of UV¯¯¯¯¯¯¯¯
is (4,3). The coordinates of one endpoint are U (11, -2). Find the coordinates of the other endpoint, V. (1 point)

Answer 3

To find the coordinates of the other endpoint V, we can use the midpoint formula. The midpoint formula states that the coordinates of the midpoint (4, 3) are the average of the two endpoint coordinates (x1, y1) and (x2, y2):

(4, 3) = [(x1 + x2) / 2, (y1 + y2) / 2]

We know that U is at (11, -2). Let's substitute these values into the midpoint formula:

(4, 3) = [(11 + x2) / 2, (-2 + y2) / 2]

Simplify the expression:

4 = (11 + x2) / 2

8 = 11 + x2

Subtract 11 from both sides:

-3 = x2

Now let's solve for the y-coordinate:

3 = (-2 + y2) / 2

Multiply both sides by 2:

6 = -2 + y2

Add 2 to both sides:

8 = y2

Therefore, the coordinates of the other endpoint V are (-3, 8).