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Answer:
ΔPQO is a right triangle
Step-by-step explanation:
Looking at the way the lines cross the grid intersections, we can see right away that the triangle is a right triangle, because the slope of OP is -2 and the slope of OQ is 1/2. These are opposite reciprocals of each other, so the segments are perpendicular. Angle O is a right angle.
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The problem asks us to look at the relationship between side lengths.
The length of OP is found from the coordinates by ...
OP² = (-1 -0)² +(2 -0)² = 1 +4 = 5
OQ² = (6 -0)² +(3 -0)² = 36 +9 = 45
PQ² = (6 -(-1))² +(3 -2)² = 49 +1 = 50
The sum of the squares of the legs is equal to the square of the longest side (5+45=50), so this triangle is a right triangle.
