Answer:
Required Value of x is x=9
Step-by-step explanation:
We are given A(x, 1), B(-3, 7), C(-5, 9), and D(5, 4) and we need to find value of x, given that AB is parallel to CD
We know that if two lines are parallel, there slope is equal.
So, if we find slope of line CD, it will be same for line AB and using slope formula we can find value of x.
The formula used to find slope is: [tex]Slope=\frac{y_2-y_1}{x_2-x_1}[/tex]
Finding Slope of line CD
Using Points C(-5, 9), and D(5, 4) the slope of line CD is:
[tex]Slope=\frac{y_2-y_1}{x_2-x_1}\\Slope=\frac{4-9}{5-(-5)}\\Slope=\frac{-5}{5+5}\\Slope=\frac{-5}{10}\\Simplifying:\\Slope=\frac{-1}{2}[/tex]
So, slope of line CD is: Slope = -1/2
Finding value of x
Using points A(x, 1), B(-3, 7) and Slope =-1/2 (Parallel lines have same slope) we can find value of x:
[tex]Slope=\frac{y_2-y_1}{x_2-x_1}\\-\frac{1}{2}=\frac{7-1}{-3-x}\\-\frac{1}{2}=\frac{6}{-3-x}\\Cross \ Multiply:\\-1(-3-x)=6*2\\3+x=12\\x=12-3\\x=9[/tex]
So, Required Value of x is x=9
