SOLUTION: The points P(−3,�6) and Q(1,�4) are two vertices of right triangle PQR . The hypotenuse of the triangle is PQ � � � � � . Point R lies in quadrant 1.

Question 1067407: The points
P(−3,�6)
and
Q(1,�4)
are two vertices of
right triangle PQR
. The hypotenuse of the triangle is
PQ
�
�
�
�
�
.
Point R lies in quadrant 1.
What are the the coordinates of point R?
Found 3 solutions by josgarithmetic, MathTherapy, ikleyn:
Answer by josgarithmetic(39620)   (Show Source): You can put this solution on YOUR website!
Whichever placement of the right angle, the hypotenuse will be the segment PQ, and this length is .

Pick the x coordinate 1 and the y coordinate 6 for the right angle point at (1,6) and this should be the point opposite the hypotenuse in quadrant 1.
Answer by MathTherapy(10553)   (Show Source): You can put this solution on YOUR website!

The points
P(−3,�6)
and
Q(1,�4)
are two vertices of
right triangle PQR
. The hypotenuse of the triangle is
PQ
�
�
�
�
�
.
Point R lies in quadrant 1.
What are the the coordinates of point R?

The point R will have the same x-coordinate as Q (1), and the same y-coordinate as P (6), so we get R as:
Answer by ikleyn(52805)   (Show Source): You can put this solution on YOUR website!
.

Draw the circle with the radius of = = and with the center at the point (-1,5) which is the midpoint of the segment connecting the given points. ALL the points of this circle (except P and Q) are potentially the vertex R of the right angled triangle PQR having PQ as the hypotenuse. All of these points that belong to QI satisfy the condition requirement. All the other answers to this post are INCORRECT.

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SOLUTION: The points P(&#8722;3,�6) and Q(1,�4) are two vertices of right triangle&#8201;PQR . The hypotenuse of the triangle is PQ � � � � � . Point R lies in quadrant 1.

SOLUTION: The points P(−3,�6) and Q(1,�4) are two vertices of right triangle PQR . The hypotenuse of the triangle is PQ � � � � � . Point R lies in quadrant 1.