Determine the triangle and classify question 4.1.2

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  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.

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