Question

use coordinate geometry to justify \\(\triangle abc \sim \triangle ade\\)

what is the slope of \\(de\\)?

\\(m = \\)

what is the slope of \\(bc\\)?

\\(m = \\)

\\(de\\) \\(bc\\)

Explanation:

⚡ Using what you learned: slope of a line

Step 1: Identify coordinates of the points

From the coordinate grid:

• Point \( D \) is at \( (3, 3) \)
• Point \( E \) is at \( (7, 1) \)
• Point \( B \) is at \( (-5, -1) \)
• Point \( C \) is at \( (5, -5) \)

Step 2: Calculate the slope of DE

Using the slope formula \( m = \frac{y_2 - y_1}{x_2 - x_1} \):

$$ m = \frac{1 - 3}{7 - 3} = \frac{-2}{4} = -\frac{1}{2} $$

Step 3: Calculate the slope of BC

Using the slope formula \( m = \frac{y_2 - y_1}{x_2 - x_1} \):

$$ m = \frac{-5 - (-1)}{5 - (-5)} = \frac{-4}{10} = -\frac{2}{5} $$

Step 4: Determine the relationship between DE and BC

Since the slopes are not equal (\(-\frac{1}{2}
eq -\frac{2}{5}\)), the lines are not parallel:

$$ DE ot\parallel BC $$

Answer:

What is the slope of \( DE \)?
\( m = -\frac{1}{2} \)

What is the slope of \( BC \)?
\( m = -\frac{2}{5} \)

Relationship:
\( DE
ot\parallel BC \)