SOLUTION: In a plane,the distance between points X and Y is 10 the distance between points X and P is 3, and the distance between points Y and Q is 4 which of the following CANNOT be the len

Question 1040775: In a plane,the distance between points X and Y is 10 the distance between points X and P is 3, and the distance between points Y and Q is 4 which of the following CANNOT be the length of PQ?
A) 2
B) 3
C) 15
D) 17
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!

Draw points X and Y 10 units apart. Then draw a circle with center point X and radius 3. P is some point on this circle. Imagine P can slide around freely on the circle but must stay on the circle.

Draw another circle with center Y and radius 4. Q will be stuck to the second circle.

Let d = distance from P to Q

If you imagine P and Q getting as far apart as possible, then the value of d would be maxed out. This only happens if P and Q lie on the line XY (extend out segment XY to get line XY). This max value of d is 3+10+4 = 17 units. I'm adding the distance from X to Y (10) to the two radii (3 and 4).
P and Q can't get any further than 17 units apart.

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The smallest value of d is d = 3. This can be found by computing 10-3-4 = 3. Basically take the distance of X to Y (10) and subtract off the two radii (3 and 4)

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So to summarize, the smallest value of d is d = 3 and the largest is d = 17. We can have distances between those two values. We cannot have any distance smaller than 3 or larger than 17.

Choice A is the answer because d = 2 is smaller than d = 3. We cannot have P and Q be 2 units apart.

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