A rectangle is drawn on a coordinate grid. Three of its four vertices are located at points (-1,-2), (-1,4), and (2,-2). What is the location of the fourth vertex?
DRAW IT !!!!!!!!
need upper right
x has to be +2
and y has to be +4
Well, if I were a rectangle I'd probably want to make a dramatic exit, so I'd put my fourth vertex on a tropical island far, far away. How about we go with coordinates (2,4) for a nice vacation spot?
To find the location of the fourth vertex of the rectangle, we need to understand the properties of a rectangle.
A rectangle is a quadrilateral in which all angles are right angles (90 degrees). This means that opposite sides of the rectangle are parallel and equal in length.
Given three vertices of the rectangle as (-1, -2), (-1, 4), and (2, -2), we can follow these steps to find the location of the fourth vertex:
1. First, we observe that the x-coordinate of the fourth vertex must be the same as the x-coordinate of the second vertex (-1, 4). This is because opposite sides of a rectangle are parallel, and thus their x-coordinates are equal.
2. Next, we observe that the y-coordinate of the fourth vertex must be the same as the y-coordinate of the third vertex (2, -2). This is because opposite sides of a rectangle are parallel, and thus their y-coordinates are equal.
3. Therefore, the coordinates of the fourth vertex are (-1, -2). This is because we know the x-coordinate is -1, and the y-coordinate is the same as the third vertex, which is -2.
So, the location of the fourth vertex is (-1, -2).
To find the location of the fourth vertex of a rectangle on a coordinate grid, we need to consider the properties of a rectangle. One property is that the opposite sides of a rectangle are parallel and equal in length.
In this case, the rectangle is defined by three vertices: (-1,-2), (-1,4), and (2,-2). Let's label these points as A(-1,-2), B(-1,4), and C(2,-2).
First, we can find the length and slope of line segment AB. The formula for the length (L) of a line segment between two points (x1,y1) and (x2,y2) is given by the distance formula:
L = sqrt((x2 - x1)^2 + (y2 - y1)^2)
Using point A(-1, -2) and B(-1, 4), we can calculate the length of AB:
L_AB = sqrt((-1 - -1)^2 + (4 - -2)^2)
= sqrt(0^2 + 6^2)
= sqrt(36)
= 6
Now, let's find the slope of line segment AB. The formula for the slope (m) of a line passing through two points (x1,y1) and (x2,y2) is given by:
m = (y2 - y1) / (x2 - x1)
Using point A(-1, -2) and B(-1, 4), we can calculate the slope of AB:
m_AB = (4 - -2) / (-1 - -1)
= 6 / 0
= undefined (division by zero is undefined)
Since the slope is undefined, line segment AB is vertical. Therefore, the fourth vertex of the rectangle must have the same x-coordinate as point C, which is 2. So, the x-coordinate of the fourth vertex of the rectangle is 2.
Since opposite sides of a rectangle are parallel, the fourth vertex must have the same y-coordinate as point A(-1, -2). So, the y-coordinate of the fourth vertex of the rectangle is -2.
Thus, the location of the fourth vertex is (2, -2).