Find the area of a rectangle if three of its corners are (-3.7, -3.1), (1.2, -3.1), and (1.2, 5.3). Hint: find the 4th corner first.
I made a rough sketch, and I bet the missing point is
(-3.7 , 5.3)
length = 1.2 - (-3.7) = 4.9
width = ...
area = length x width
= ...
How do you solve for the length you don't have to slove it but what would the formula be ?...
hard to believe your class materials don't include the formula for finding the distance between two points. Think Pythagorean Theorem.
To find the area of a rectangle using its coordinates, we need to find the length and width of the rectangle first. We can do this by finding the coordinates of the fourth corner. Since a rectangle has four right angles, we know that the opposite corners of a rectangle have the same x-coordinate or the same y-coordinate.
In this case, two of the corners, (-3.7, -3.1) and (1.2, 5.3), have the same y-coordinate of -3.1. Therefore, the missing corner should also have a y-coordinate of -3.1.
Similarly, we can see that the other two corners, (-3.7, -3.1) and (1.2, -3.1), have the same x-coordinate of -3.7. Hence, the missing corner should have an x-coordinate of 1.2.
Therefore, the coordinates of the fourth corner are (1.2, -3.1).
Now, we can calculate the length and width of the rectangle. The length is the difference between the x-coordinates of two adjacent corners, which is 1.2 - (-3.7) = 4.9 units. The width is the difference between the y-coordinates of the same two adjacent corners, which is (-3.1) - (-3.1) = 0 units.
Since the width is 0 units, we can conclude that this is not a rectangle but rather a line segment. The area of a line segment is always zero.
Therefore, the area of the given figure is zero.