Question

The coordinates of the vertices of quadrilateral ABCD are A(−1, −1) , B(−3, 3) , C(1, 5) , and D(5, 2) .

Drag and drop the choices into each box to correctly complete the sentences.

The slope of AB¯¯¯¯¯ is , the slope of BC¯¯¯¯¯ is , the slope of CD¯¯¯¯¯ is , and the slope of AD¯¯¯¯¯ is . Quadrilateral ABCD is because .

Answer 1

The calculate a slope we use the equation:

`m=(y_(2)-y_(1))/(x_(2)-x_(1))`; where
`m` is the slope,
`(x_(1);y_(1))` are the coordinates of the first point, and
`(x_(2);y_(2))` are the coordinates of the second point. The first and second points are arbitrary, we just choose a specific order b our own.

So, the problem is asking for the slope of AB, BC, CD and AD, which are sides of a quadrilateral figures. Now, we use each coordinates, replace them is the slope equations and get the result.

The slope of AB:

Coordinates are
`A(-1, -1)` and
`B(-3, 3)`.

`m_(AB) =(y_(2)-y_(1))/(x_(2)-x_(1))=(3-(-1))/(-3-(-1))=(3+1)/(-3+1) =(4)/(-2)=-2`

The slope of BC:

Coordinates are
`B(-3, 3)` and
`C(1, 5)`

`m_(BC) =(y_(2)-y_(1))/(x_(2)-x_(1))=(5-3)/(1-(-3)) =(2)/(1+3)=(2)/(4)=(1)/(2)`

The slope of CD:

Coordinates are
`C(1, 5)` and
`D(5, 2)`

`m_(CD) =(y_(2)-y_(1))/(x_(2)-x_(1))=(2-5)/(5-1)=(-3)/(4)`

The slope of AD:

Coordinates are
`A(-1, -1)` and
`D(5, 2)`

`m_(AD) =(y_(2)-y_(1))/(x_(2)-x_(1))=(2-(-1))/(5-(-1)) =(2+1)/(5+1)=(3)/(6)=(1)/(2)`

According to these results, sides AB and BC are perpendicular because the slopes have opposite signs and inverse numbers. In addition, BC and AD are parallel, because they have the same slope. The graph is attached.

Answer 2

The answer is:

`m_(AB)=-2`

`m_(BC)=(1)/(2)`

`m_(CD)=-(3)/(4)`

`m_(AD)=-(3)/(4)`

It is a trapezium because it has two parallel sides.

1. The formula for calculate the slope is the following:

`m=(y_2-y_1)/(x_2-x_1)`

2. Therefore, the slope of AB is:

`m_(AB)=(3-(-1))/(-3-(-1))\\m_(AB)=-2`

3. The slope of BC is:

`m_(BC)=(5-3)/(1-(-3))\\m_(BC)=(1)/(2)`

4. The slope of CD is:

`m_(CD)=(2-5)/(5-1)\\m_(CD)=-(3)/(4)`

5. The slope of AD is:

`m_(AD)=(2-(-1))/(5-(-1))\\m_(AD)=(1)/(2)`

The slope of AD and BC are equal, therefore AD and BC are parallel, so the quadrilateral is a trapezium.