Shane has a segment with endpoints C3 4 and D11 3 that is di

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? 3 over 5 5 over 3 3 over 8 5 over 8

Solution

Given that CE and DE form a 3:5 ratio

Here is the internal point of division E(x,y).

x = [5(3) + 3(11)]/(5 + 3) = 6
y = [5(4) + 3(3)]/(5 + 3) = 29/8
E(6, 29/8)

let m:n be the fraction that will let him find the x-coordinate for point E.

We know that x-coordinate for point E = 6

The formula to find the point which is dividing the line segment AB internally in the ratio m:n is given by

( x,y ) = { mx2+nx1/m+n , my2 +ny1/m+n }

x = mx2+nx1/m+n

=> 6 = 3m + 11n/(m+n)

=> 6 (m+n) = 3m + 11n

=> 3m = 5n

=> m/5 = n/3

So , the ratio will be = 5 over 3 (5:3)