Question

Hamid is making a stained-glass window. Heneeds a piece of glass that is a perfect parallelogram.Hamid lays a piece of glass that he has cut on acoordinate grid. Show that the glass is in the shape of a parallelogram.

Answer 1

The slopes of the top and bottom lines are equal, so also is the slope of the sides; and this indicates that the sides facing each other are parallel, thereby showing that the glass is in the shape of a parallelogram

For the glass to be a parallelogram, there are some inportant properties that must be followed;

The property is that the sides facing each other must be parallel

The top and bottom must be parallel

If two lines are parallel, the value of their slopes will be equal

Let us start with the top and bottom;

We use the equation of the slope at each line;

`\begin{gathered} m\text{ = }(y_2-y_1)/(x_2-x_1) \\ m_1=\text{ }(3-3)/(8+5)\text{ = 0} \\ \\ m_2=\text{ }\frac{-2+2}{11\text{ + 2}}\text{ = 0} \end{gathered}`

The slope of the bottom and top lines are equal which shows that they are parallel

For the sides, we have that;

`\begin{gathered} m_3\text{ = }(-2-3)/(-2-(-5))\text{ = }(-5)/(3) \\ \\ m_4\text{ = }(-2-3)/(11-8)\text{ = }(-5)/(3) \end{gathered}`