Question

point e is drawn on the graph so that line ef is parallel to line cd.
if the coordinates of point e are \\((-4, y)\\), what is the value of \\(y\\)?
-8
-4
0
8

Explanation:

Identify coordinates of points C and D

We read the coordinates of points \(C\) and \(D\) from the given coordinate plane:

• Point \(C\) is located at \((-10, -2)\).
• Point \(D\) is located at \((10, 6)\).

Calculate the slope of line CD

Using the Slope Formula:

$$ m = \frac{y_2 - y_1}{x_2 - x_1} $$

Substitute the coordinates of \(C(-10, -2)\) and \(D(10, 6)\):

$$ m_{CD} = \frac{6 - (-2)}{10 - (-10)} = \frac{8}{20} = \frac{2}{5} $$

Determine the slope of line EF

Since line \(EF\) is parallel to line \(CD\), their slopes must be equal:

$$ m_{EF} = m_{CD} = \frac{2}{5} $$

Identify coordinates of point F

From the graph, we locate point \(F\) at:

• \(F(6, -4)\)

Solve for the y-coordinate of point E

Point \(E\) has coordinates \((-4, y)\). Using the slope formula for line \(EF\):

$$ m_{EF} = \frac{y_F - y_E}{x_F - x_E} $$

Substitute the known values:

$$ \frac{2}{5} = \frac{-4 - y}{6 - (-4)} $$

$$ \frac{2}{5} = \frac{-4 - y}{10} $$

Multiply both sides by 10:

$$ 4 = -4 - y $$

$$ y = -8 $$

Answer:

• (A) -8 (Correct answer)
• (B) -4
• (C) 0
• (D) 8