Answer :
To solve this question, we will perform the following steps:
Step 1: Graph the trapezoid
To graph the trapezoid, plot the points A, B, C, and D on a coordinate grid based on their given coordinates.
- Point A is at (6, 5).
- Point B is at (8, -2).
- Point C is at (-4, -2).
- Point D is at (-2, 5).
Once the points are plotted, we can draw lines to connect them in the order given to form the trapezoid.
Step 2: Find the lengths of bases CB and AD
a. The length of the bottom base (segment CB) can be found using the distance formula between two points \( (x_1, y_1) \) and \( (x_2, y_2) \) in a plane:
\[ \text{Distance} = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2} \]
For base CB, the coordinates are C(-4, -2) and B(8, -2). Applying the distance formula:
\[ \text{Length of CB} = \sqrt{(8 - (-4))^2 + ((-2) - (-2))^2} \]
\[ \text{Length of CB} = \sqrt{(8 + 4)^2 + (0)^2} \]
\[ \text{Length of CB} = \sqrt{12^2 + 0^2} \]
\[ \text{Length of CB} = \sqrt{144} \]
\[ \text{Length of CB} = 12 \] (using grid units)
Similarly, find the length of the top base (segment AD). The coordinates are A(6, 5) and D(-2, 5). So,
\[ \text{Length of AD} = \sqrt{(6 - (-2))^2 + (5 - 5)^2} \]
\[ \text{Length of AD} = \sqrt{(6 + 2)^2 + (0)^2} \]
\[ \text{Length of AD} = \sqrt{8^2 + 0^2} \]
\[ \text{Length of AD} = \sqrt{64} \]
\[ \text{Length of AD} = 8 \] (using grid units)
b. To find the height (the distance between the two bases), we can observe that since B and C, have the same y-coordinate, the segment is horizontal, and the height is simply the difference in the y-coordinates of A (or D) and B (or C). This can also be seen as the vertical distance from A to the line BC.
Given that point A has a y-coordinate of 5 and B has a y-coordinate of -2, the height (h) is:
\[ h = |y_A - y_B| \]
\[ h = |5 - (-2)| \]
\[ h = |5 + 2| \]
\[ h = 7 \] (using grid units)
In conclusion:
- The length of the bottom base CB is 12 grid units.
- The length of the top base AD is 8 grid units.
- The height of the trapezoid is 7 grid units.
