Question

Shane has a segment with endpoints C(3, 4) and D(11, 3) that is divided by a point E such that CE and DE form a 3:5 ratio. He knows that the distance between the x-coordinates is 8 units. Which of the following fractions will let him find the x-coordinate for point E?

Answer 1

x - coordinate of Point E = 6

Step-by-step explanation:

C(3, 4) and D(11, 3)

point E such that CE and DE form a 3:5 ratio

coordinates of E   =  ( 3 *11  + 5 * 3)/(3 + 5)   ,  (3*3  + 5 * 4)/(3 + 5)

= (33 + 15)/8   ,  (9 + 20)/8

= 48/8  ,  29/8

=  6  ,  3.625

Following fractions are not given

x - coordinate of Point E is 6

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Answer 2

Answer:

The fraction would be 3/8

Step-by-step explanation:

Since, when a segment having endpoints $(x_1, y_1)$ and $(x_2, y_2)$ is divided by a point in the segment in the ratio of m:n,

Then the x-coordinate of the point is,

$x = x_1 + \frac{m}{m+n}(x_2-x_1)$

Thus, the fraction that is used to find the x-coordinate would be $\frac{m}{m+n}$

Here, m = 3 and n = 5,

Since,

$\frac{3}{3+5}=\frac{3}{8}$

Hence, the required fraction would be 3/8.

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