Question

Figure ABCDE has vertices A(−3, 3), B(2, 3), C(5, −2), D(0, −3), and E(−3, −2). Plot the points on your own coordinate grid and connect the points in alphabetical order. Decompose Figure ABCDE into rectangles and triangles.

Part A: How many triangles and rectangles did you make? (1 point)

Part B: Use Figure ABCDE created on your coordinate grid to find the lengths, in units, of Sides AB and AE. (4 points)

Part C: What is the area of Figure ABCDE? Show your work.

Answer 1

help me!!!

Answer 2

Hi, and welcome to QuestionCove!
I've plotted the points as described in the question. By using the coordinates given for each point, we can see where each point is supposed to go on the grid

Answer 3

The question then asks us to connect the points in alphabetical order: A->B->C->D->E
Please excuse the typo; point "E" at (0,-3) is supposed to be point "D"

Answer 4

We're then asked to "decompose Figure ABCDE into triangles and rectangles"
There are many possible ways of doing this, and I'll try to show the approach I took in this drawing
We can refer to this figure to answer parts A B and C of the question, although you may come up with your own version of the drawing as well

Answer 5

Question A: In my version of the drawing, figure ABCDE is split into 1 rectangle (connecting E, A, B, and the point at (2,-2)) and 2 triangles (CDE and BC(2,-2))

Question B: To find the distance between two points on a grid, use the equation
\[Distance = \sqrt{(x _{1}-x _{2}) + (y _{1}-y _{2})}\] Side AB connects points at (-3,3) and (2,3). Using the equation gives us a distance of 5 between these points; you can also see from the drawing that point B is exactly 5 units to the right of point A. So AB is 5 units long.
Similarly, we could use the equation for points A and E or see that point A is exactly 5 units above point E; either way, we find that AE is 5 units long

Question C: The area of figure ABCDE is equal to the combined area of the rectangle and triangles that make up the figure. The rectangle is 5 by 5, which has an area of 25 units; triangle CDE has an area of (8*1)/2, which is equal to 4; triangle BC(2,-2) has an area of (5*3)/2, which is equal to 7.5; the total area of the figure is 25+4+7.5 = 36.5