A rectangle on a coordinate plane has vertices Q(Negative 1, 1), R(6, 1), S(6, Negative 8), and T(Negative 1, Negative 8). What are the dimensions of the rectangle?

To find the dimensions of the rectangle, you need to calculate the lengths of its sides. The length of the horizontal side (width) can be found by determining the distance between Q and R or between S and T, and the length of the vertical side (height) can be found by determining the distance between Q and T or between R and S.

Looking at the coordinates for Q(-1, 1) and R(6, 1), you can see that the y-coordinates are the same. This means that QR is a horizontal line segment. The width of the rectangle is the distance between the x-coordinates of Q and R, which is the absolute difference between -1 and 6. So, the width is |6 - (-1)| = |6 + 1| = 7 units.

Now, look at the coordinates for Q(-1, 1) and T(-1, -8). Here, the x-coordinates are the same. This means that QT is a vertical line segment. The height of the rectangle is the distance between the y-coordinates of Q and T, which is the absolute difference between 1 and -8. So, the height is |1 - (-8)| = |1 + 8| = 9 units.

So, the rectangle has a width of 7 units and a height of 9 units.

Extra: Understanding coordinates and distances on the coordinate plane is essential in geometry. On the coordinate plane, each point has two values: an x-coordinate (which shows horizontal position) and a y-coordinate (which shows vertical position). The x-coordinate indicates how far to the right (positive) or to the left (negative) the point is from the vertical axis, also known as the y-axis. The y-coordinate indicates how far up (positive) or down (negative) the point is from the horizontal axis, known as the x-axis.

The distance between two points that share the same y-coordinate (horizontal distance) can be determined by subtracting the x-coordinates of the two points. If the two points share the same x-coordinate (vertical distance), the distance between them is found by subtracting the y-coordinates of the two points. In both cases, the absolute value of the difference gives you the distance, since distance cannot be negative.

Rectangles on the coordinate plane are easy to analyse because their sides are either vertical or horizontal, which means they are parallel to the axes. This property of rectangles can be used to your advantage when trying to determine their dimensions or when solving other related problems.