Question

Line segments, AB,BC,CD,DA create the quadrilateral graphed on the coordinate grid above. The equations for two of the four line segments are given below. Use the equations of the line segments to answer the questions that follow. AB: y = -x + 1 BC: y = -3x + 11

Answer 1

The equations of the line segments are,

`\begin{gathered} AB\colon y=(1)/(3)x+1 \\ BC\colon y=-3x+11 \end{gathered}`

Calculate the equations of CD and AD.

The equation of line Cd is,

`\begin{gathered} (y-(-3))=(-1+3)/(4+2)(x+2) \\ y+3=(1)/(3)(x+2) \\ 3y=x-7 \end{gathered}`

The equation of the line AD is,

`\begin{gathered} y-0=(-3-0)/(-2+3)(x+3) \\ y=-3x-9 \end{gathered}`

1)If two lines are parallel slope will be equal and perpendicular product of slope will be -1.

From the equation, the slope of AB is 1/3

From the equation, the slope of Cd is 1/3.

So, they are parallel.

2)The slope of AB is 1/3.

The slope of BC is -3.

The product of two slopes is -1. Therefore, AB is perpendicular to BC.

3) The slope of AB is 1/3 and slope of AD is -3. Since, the product is -1, they are perpendicular.

Another pair of line segments that are perpendicular to each other is AB and AD.