Gina plotted the points (−3, 4), (4, 4), (−3, −2), and (4, −2)
on the coordinate plane.
A graph is shown in the xy-plane. The values on the x-axis ranges from negative 8 to 8 in increments of 2 and the values on the y-axis ranges from negative 8 to 8 in increments of 2. Four points are marked on the graph whose coordinates are (negative 3, 4), (4, 4), (negative 3, negative 2), and (4, negative 2).
A. Determine the height of the quadrilateral.
B. Determine the length of the quadrilateral.
C. Gina said the points formed a square. Is she correct? Explain your reasoning.
A. To determine the height of the quadrilateral, we look at the difference in the y-coordinates of the points. Since two points have a y-coordinate of 4 and the other two have a y-coordinate of -2, the height is 4 - (-2) = 6 units.
B. To determine the length of the quadrilateral, we look at the difference in the x-coordinates of the points. Since two points have an x-coordinate of -3 and the other two have an x-coordinate of 4, the length is 4 - (-3) = 7 units.
C. For the points to form a square, the length and height should be equal. Since the length is 7 and the height is 6, they are not equal, so Gina is not correct. The points do not form a square. The quadrilateral is a rectangle, because it has four 90-degree angles and opposite sides are equal in length.
Is that the right explanation Bot?
Yes, that is the correct explanation.
Can somebody help me with a question that i have?
Of course! What is your question?
Consider points A to F shown on the coordinate plane.
A graph is shown in the xy-plane. The values on the x-axis ranges from negative 8 to 8 in increments of 2 and the values on the y-axis ranges from negative 8 to 8 in increments of 2. Six points, Upper A, Upper B, Upper C, Upper D, Upper E, and Upper F are marked on the graph. The point Upper A is 4 units above the x-axis and 6 units to the left of the y-axis, the point Upper B is 3 units above the x-axis and 5 units to the right of the y-axis, the point Upper C is 7 units below the x-axis and 5 units to the left of the y-axis, the point Upper D is 2 units below the x-axis and 8 units to the right of the y-axis, the point Upper E is on the x-axis and 7 units to the left of the y-axis, and the point Upper F is on the y-axis and 6 units above the x-axis.
What are the coordinates of points C, D, and E?
The coordinates of point C are (-5,-7) because it is 5 units to the left of the y-axis and 7 units below the x-axis.
The coordinates of point D are (8,-2) because it is 8 units to the right of the y-axis and 2 units below the x-axis.
The coordinates of point E are (-7,0) because it is 7 units to the left of the y-axis and on the x-axis (where y-coordinate is 0).
For the coordinates of C, does the -7 go before the -5?
No, the x-coordinate always comes before the y-coordinate. So for the coordinates of point C, it is (-5,-7) and not (-7,-5).
Ok, thank you. I also have another question that is difficult
On the coordinate plane shown, points A
(
−
5
,
−
6
)
, B
(
2
,
−
6
)
, C
(
8
,
5
)
, and D
(
−
7
,
5
)
are plotted and connected with line segments to form a trapezoid.
A graph is shown in the xy-plane. The values on the x-axis ranges from negative 8 to 8 in increments of 2 and the values on the y-axis ranges from negative 8 to 8 in increments of 2. Four points Upper A, Upper B, Upper C, and Upper D are marked on the graph with coordinates (negative 5, negative 6), (2, negative 6), (8, 5), and (negative 7, 5) respectively. The four points are joined together to form a trapezium UpperWord ABCD.
What is the height of the trapezoid?