Please check my answer..
Find a point E on segment CD such that the ratio of segment CE is 5/8
C is placed on (-9) and point D is placed on 7.
A. -8
B.-1~~~
C. 1
D. -3
CD = 7-(-9) = 16 , or count them
CE = (5/8)(16) = 10
now count over 10 units from C
E ---> -9 + 10 = 1
To find the point E on segment CD such that the ratio of segment CE is 5/8, we need to determine the coordinates of E.
First, let's calculate the length of segment CD. The coordinates of point C are (-9, 0), and the coordinates of point D are (7, 0). We can find the length of CD using the distance formula:
d = sqrt((x2 - x1)^2 + (y2 - y1)^2)
d = sqrt((7 - (-9))^2 + (0 - 0)^2)
d = sqrt((16)^2)
d = sqrt(256)
d = 16
Now, let's find the length of segment CE. We know that the ratio of CE to CD is 5/8, so:
CE/CD = 5/8
CE/16 = 5/8
Cross-multiplying, we get:
8 * CE = 5 * 16
8CE = 80
CE = 80/8
CE = 10
Since C is placed at x = -9, to find the x-coordinate of E, we need to traverse a distance of 10 units from C towards D. Since we are moving from -9 towards positive x-values, the x-coordinate of E will be -9 + 10 = 1.
Therefore, the correct answer is C. 1.