with vertices A, B, C, D to be determined. The vertices of the rectangle are such that the rectangle contains the triangle, and all its sides are either parallel or perpendicular to the axes.
Firstly, we need to find the x-coordinates and y-coordinates from all the vertices of the triangle.
The x-coordinates from vertices P,Q,R are -3, -2, and -5 respectively. The y-coordinates from P,Q,R are 5, 9, and 8 respectively.
Now it is required to find the minimum and maximum values from these sets of x-coordinates and y-coordinates, as these will become the coordinates of our rectangle vertices.
The smallest x-coordinate is -5 and largest is -2. Therefore, the x-coordinates of the rectangle will be at -5 and -2.
On the other hand, smallest y-coordinate is 5 and the largest is 9. Therefore, the y-coordinates of the rectangle will be at 5 and 9.
Hence, the vertices of the rectangle are determined as follows:
A, which is at the bottom left of the rectangle, is at the point of minimum x and y values, i.e., A(-5, 5).
B, which is at the top left of the rectangle, is positioned at the point of minimum x and maximum y, i.e., B(-5, 9).
C, which is at the top right of the rectangle, is at the point of maximum x and y values, i.e., C(-2, 9).
Finally, D, which is at the bottom right of the rectangle, is at the point of maximum x and minimum y, i.e., D(-2, 5).
To sum up, the coordinates of the rectangle that contains Triangle PQR are A(-5, 5), B(-5, 9), C(-2, 9), D(-2, 5).