Answer:
Right rectangle.
Explanation:
The rectangle will be a right rectangle only if the opposite sides are parallel to each other.
This means that RQ should be parallel to ST
And RS should be parallel to QT
Each side can be represented by a line with a restricted domain, and we know that two lines are parallel only if they have the same slope.
Remember that the slope relates to how a change in the x-value makes a change in the y-value.
Then if two segments have, for a fixed change in the x-value, the same change in the y-value, we can conclude that those segments are parallel.
So here to see if the lines are parallel, we just need to compare the changes between the endpoints of each segment.
Let's start with segments QR and TS
First let's look at the segment QR, and let's try to find the difference in the coordinates between R and Q.
In the graph, we can see that R is 3 units above and one unit to the right of Q.
Now let's do the same for the other segment:
In the graph, we also can see that S is 3 units above and one unit to the right of T.
So these two lines will have the same slope:
Only with this, we can conclude that sides QR and TS are parallel.
Now with the other two segments: RS and QT.
Similar to the above case, for the segment RS we can see that S is 4 units at the right and 1 unit below R.
For the segment QT, we can see that T is 4 units at the right and one unit below Q.
So segments RS and QT have the same slope, thus, the segments are parallel.
Then we can conclude that this is a right rectangle.