Question

which point on the y - axis lies on the line that passes through point g and is parallel to line df? (-2,0) (0,-2) (0,4) (4,0)

Explanation:

Step1: Find the slope of line DF

The coordinates of D are (-1,-3) and of F are (2,3). The slope formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$. So, $m_{DF}=\frac{3-(-3)}{2 - (-1)}=\frac{6}{3}=2$.

Step2: Use the point - slope form with point G

Assume the coordinates of G are (-4,-4). The point - slope form of a line is $y - y_1=m(x - x_1)$. Since the line we want is parallel to DF, its slope $m = 2$. Using point G, we have $y-(-4)=2(x - (-4))$, which simplifies to $y + 4=2(x + 4)$.

Step3: Find the y - intercept

To find the point on the y - axis, we set $x = 0$. Substituting $x = 0$ into $y+4=2(x + 4)$ gives $y+4=2(0 + 4)$, so $y+4 = 8$ and $y=4$.

Answer:

$(0,4)$