Question

slope of ad:
slope of dc:
slope of bc:
explain why abcd is a parallelogram.

identify which lines are perpendicular.

1. ( y = 5 ; y = \frac { 1 } { 8 } x ; x = 2 ; y = 8 x - 5 )

1. ( y = - 2 ; y = - \frac { 1 } { 2 } x - 4 ; y - 4 = 2 ( x + 3 ) ; y = - 2 x )

1. show that abc is a right triangle.

Explanation:

Answer:

1. \( y=\frac{1}{8}x \) and \( y = 8x - 5 \) are not perpendicular. \( y = 5 \) (horizontal line) and \( x = 2 \) (vertical line) are perpendicular
2. \( y=-\frac{1}{2}x - 4 \) and \( y - 4=2(x + 3) \) (since \( m_1=-\frac{1}{2}\), \(m_2 = 2\), \(m_1\times m_2=- 1\)) are perpendicular
3. Calculate slopes: slope of \(AB=\frac{-1+2}{2 + 2}=\frac{1}{4}\), slope of \(BC=\frac{2 + 2}{-3+2}=-4\), slope of \(AC=\frac{-1 - 2}{2+3}=-\frac{3}{5}\). Since slope of \(AB\times\) slope of \(BC=\frac{1}{4}\times(-4)=-1\), \(AB\perp BC\), so \(ABC\) is a right - triangle