Answer:
C. 5 units
Explanation:
Point Q is 4 grid squares left of point P, and 3 grid squares down from point P. The distance between them must be more than 4 and less than 4+3=7. There is only one answer choice that qualifies: 5 units.
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The distance is usually found using the Pythagorean theorem. Here, we can draw a right triangle by connecting P and Q for the hypotenuse, and by drawing along the grid lines to make perpendicular legs that are 3 and 4 units long. The Pythagorean theorem will tell you ...
PQ² = 3² +4²
PQ² = 25 . . . . . . . evaluate the sum
PQ = √25 = 5 . . . take the square root
The distance from P to Q is 5 units.
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Additional comments
This 3-4-5 right triangle is a Pythagorean triple that shows up in a lot of algebra, geometry, and trigonometry problems. It is worthwhile to remember this triple, and to be able to identify multiples of it, such as 6-8-10.
As we noted at the beginning, the length of the hypotenuse of a right triangle is always more than the longest leg and less than the sum of the leg lengths. This fact alone will help you solve many triangle and distance problems. (Of course, you know this if you have ever cut across a corner to walk a shorter distance.)