SOLUTION: Find the equation of straight line that passes through point L and M were L is the mid-point of the straight line joining A(-1, 6) to B(5,4) and M is the mid-point of the line join

Algebra ->  Equations -> SOLUTION: Find the equation of straight line that passes through point L and M were L is the mid-point of the straight line joining A(-1, 6) to B(5,4) and M is the mid-point of the line join      Log On


   

Question 1139062: Find the equation of straight line that passes through point L and M were L is the mid-point of the straight line joining A(-1, 6) to B(5,4) and M is the mid-point of the line joining C(-5, -1) to D(3, -1)
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
A(-1,6)
B(5,4)
+L%5Bx%5D+=+%28-1%2B5%29%2F2%29%0D%0A%7B%7B%7B+L%5Bx%5D+=+2+
and
+L%5By%5D+=+%286%2B4%29%2F2+
+L%5By%5D+=+5+
----------------------------
C(-5,-1)
D(3,-1)
+M%5Bx%5D+=+%28-5%2B3%29%2F2+
+M%5Bx%5D+=+-1+
and
+M%5By%5D+=+%28-1%2B%28-1%29%29%2F2+
+M%5By%5D+=+-1+
---------------------------
The midpoints are:
L( 2,5)
M(-1,-1)
Use general point-slope formula
+%28+5+-%28-1%29+%29+%2F+%28+2+-%28-1%29+%29+=+%28+y+-%28-1%29+%29+%2F+%28+x+-%28-1%29+%29+
+6%2F3+=+%28+y+%2B+1+%29+%2F+%28+x+%2B+1+%29+
+2+=+%28+y+%2B+1+%29+%2F+%28+x+%2B+1+%29+
+y+%2B+1+=+2%2A%28+x+%2B+1+%29+
+y+%2B+1+=+2x+%2B+2+
+y+=+2x+%2B+1+ answer
----------------------------
check:
A(-1,6)
B(5,4)
+%28+6+-+4+%29%2F%28+-1+-+5+%29+=+%28+y+-+4+%29+%2F+%28+x+-+5+%29+
+2%2F%28-6%29+=+%28y-4%29%2F%28x-5%29+
+-1%2F3+=+%28+y-4+%29%2F%28+x-5+%29+
+-%28+x-5+%29+=+3%2A%28+y+-+4+%29+
+-x+%2B+5+=+3y+-+12+
+3y+=+-x+%2B+17+
+y+=+%28-1%2F3%29%2Ax+%2B+17%2F3+
and
C(-5,-1)
D(3,-1)

+%28+-1+%2B1+%29+%2F+%28+-2+%29+=+%28+y+%2B+1+%29+%2F+%28+x+%2B+3+%29+
+%28+y+%2B+1+%29%2F%28+x+%2B+3+%29+=+0+
+y+%2B+1+=+0+
+y+=+-1+
-----------------------
Here is a plot of the 3 lines: