A segment with endpoints C (3,4) and D (11,3) is divided by a point E such that CE and DE form a 3:5 ratio. Find E.
let E(x,y) be your point
use ratios ...
for the x:
(x-3)/(11-3) = 3/8
8x-24 = 24
8x = 48
x = 6
for the y:
(y-4)/(3-4) = 3/8
8y - 32 = -3
8y = 29
y = 29/8
E is (6,29/8)
Thank you so much reiny : )
What’s the answer
3/8?
To find the coordinates of point E, we need to divide the segment CD into two parts that are in a 3:5 ratio.
Step 1: Find the distance between points C and D.
Using the distance formula, we can calculate the distance between two points in a coordinate plane.
Distance formula:
d = √((x2 - x1)^2 + (y2 - y1)^2)
Using points C (3, 4) and D (11, 3):
d = √((11 - 3)^2 + (3 - 4)^2)
= √(8^2 + (-1)^2)
= √(64 + 1)
= √65
So, the distance between C and D is √65.
Step 2: Determine the length of CE and DE.
Since we have a 3:5 ratio, we can express the length of CE as 3x and DE as 5x, where x is a common factor.
We know that CE + DE = √65.
So, 3x + 5x = √65.
8x = √65.
Dividing both sides by 8:
x = (√65)/8.
Step 3: Calculate the coordinates of E.
To find the coordinates of point E, we take the x-coordinate of D and subtract 5 times x, as well as the y-coordinate of D and subtract 5 times x.
x-coordinate of E = 11 - (5 * (√65)/8)
y-coordinate of E = 3 - (5 * (√65)/8)
Therefore, the coordinates of point E are:
E ((11 - 5 * (√65)/8), (3 - 5 * (√65)/8))
Simplifying the coordinates further may be possible.