Find the coordinate that divides the directed line segment from A(-2,-4) to B(8,1) in the ratio of 2 to 3
Accepted Solution
A:
we have that A(-2,-4) B(8,1)
let M-------> the coordinate that divides the directed line segment from A to B in the ratio of 2 to 3
we know that
A--------------M----------------------B 2 3 distance AM is equal to (2/5) AB distance MB is equal to (3/5) AB so
step 1 find the x coordinate of point M Mx=Ax+(2/5)*dABx where Mx is the x coordinate of point M Ax is the x coordinate of point A dABx is the distance AB in the x coordinate Ax=-2 dABx=(8+2)=10 Mx=-2+(2/5)*10-----> Mx=2
step 2 find the y coordinate of point M My=Ay+(2/5)*dABy where My is the y coordinate of point M Ay is the y coordinate of point A dABy is the distance AB in the y coordinate Ay=-4 dABy=(1+4)=5 Mx=-4+(2/5)*5-----> My=-2