+4 What is the value of x so that the line segment with end points A(x,1) and B(2,-3) is parallel to the line segment with end points C(-5,2) and D(-3,5)?
+23251 Two lines are parallel if they have the same slope.
The formula for slope is: ( y2 - y1 ) / ( x2 - x1 )
The slope for AB is: ( -3 - 1 ) / ( 2 - x )
The slope for CD is: ( 5 - 2 ) / ( -3 - -5 )
Setting these slopes equal to each other: ( -3 - 1 ) / ( 2 - x ) = ( 5 - 2 ) / ( -3 - -5 )
Simplifying: -4 / (2 - x) = 3 / 2
Cross-multiplying: -8 = 6 - 3x
Solving: 3x = 14
x = 4 2/3
