Question

which point on the x - axis lies on the line that passes through point c and is parallel to line ab? (1,0) (1,1) (0,2) (2,0)

Explanation:

Step1: Find the slope of line \(AB\)

Let \(A(-4,0)\) and \(B(2,-3)\). The slope formula is \(m=\frac{y_2 - y_1}{x_2 - x_1}\).
\(m_{AB}=\frac{-3 - 0}{2-(-4)}=\frac{-3}{6}=-\frac{1}{2}\)

Step2: Use the point - slope form to find the equation of the line passing through \(C(-2,2)\)

The point - slope form is \(y - y_1=m(x - x_1)\). Here \(m =-\frac{1}{2}\) and \((x_1,y_1)=(-2,2)\)
\(y - 2=-\frac{1}{2}(x + 2)\)
Expand: \(y-2=-\frac{1}{2}x - 1\)
\(y=-\frac{1}{2}x+1\)

Step3: Find the \(x\) - intercept (where \(y = 0\))

Set \(y = 0\): \(0=-\frac{1}{2}x + 1\)
\(\frac{1}{2}x=1\), then \(x = 2\)

Answer:

\((2,0)\)