# The Right Angled Triangle PQR is To Be Constructed

Right triangle PQR is to be constructed in the xy-plane so that the right angle is at P and PR is parallel to the x-axis. The x- and y-coordinates of P, Q, and R are to be integers that satisfy the inequalities -4 <= x <= 5 and 6<= y<= 16. How many different triangles with these properties could be constructed? (A) 110

## The Right Angled Triangle PQR is To Be Constructed FAQ

Right triangle PQR is to be constructed in the xy-plane so that the right angle is at P andline PR is parallel to the x-axis. The x and y coordinates of P, Q, and R are to be integersthat satisfy the inequalities: ?4 ? x ? 5 and 6 ? y ?16. https://www.transtutors.com/questions/right-triangle-pqr-is-to-be-constructed-in-the-xy-plane-so-that-the-right-angle-is-a-842161.htm

Stage 1: Select any point where the right angle will be (point P).

The point can be selected from a 10×11 grid. So, there 110 points to choose from.
This means that stage 1 can be completed in 110 ways.

Stage 2: Select a point that is on the same horizontal line as the first point. This point will be point R.

The 2 legs of the right triangle are parallel to the x- and y-axes.
The first point we select (in stage 1) dictates the y-coordinate of point R.
In how many ways can we select the x-coordinate of point R?
Well, we can choose any of the 10 coordinates from -4 to 5 inclusive EXCEPT for the x-coordinate we chose for point P (in stage 1).
So, there are 9 coordinates to choose from.
This means that stage 2 can be completed in 9 ways.

Stage 3: Select a point that is on the same vertical line as the first point. This point will be point Q.

The 2 legs of the right triangle are parallel to the x- and y-axes.
The first point we select (in stage 1) dictates the x-coordinate of point Q.
In how many ways can we select the y-coordinate of point Q?
Well, we can choose any of the 11 coordinates from 6 to 16 inclusive EXCEPT for the y-coordinate we chose for point P (in stage 1).
So, there are 10 coordinates to choose from.

This means that stage 3 can be completed in 10 ways.