Line AB is parallel to line CD for A(4, -5), B(-2, -3), C(x, -2), D(6, y). Find a set of possible values for x and y.
AB has slope 2/-6 = -1/3
So,
(y+2)/(6-x) = -1/3
3y+6 = x-6
x=3y+12
So, pick any y and that will give you an x.
To determine if line AB is parallel to line CD, we need to examine their slopes.
The slope of a line can be calculated using the formula:
m = (y2 - y1) / (x2 - x1)
For line AB with points A(4, -5) and B(-2, -3), we have:
mAB = (-3 - (-5)) / (-2 - 4)
= (-3 + 5) / (-2 - 4)
= 2 / (-6)
= -1/3
For line CD with points C(x, -2) and D(6, y), we have:
mCD = (y - (-2)) / (6 - x)
= (y + 2) / (6 - x)
Since line AB is parallel to line CD, their slopes should be equal.
Hence, we can set up an equation and solve for the unknown values of x and y.
-1/3 = (y + 2) / (6 - x)
To find a set of possible values for x and y, we need to find values that satisfy this equation.
Clearing the fraction:
-1(6 - x) = y + 2
-6 + x = y + 2
x - y = 8
From this equation, we can see that x - y should be equal to 8, regardless of the specific values of x and y.
Therefore, a set of possible values for x and y that make line AB parallel to line CD is any pair of numbers where their difference is 8. For example, (10, 2), (16, 8), and (-2, -10) are all possible solutions.