6th Grade Math Textbook, Fundamentals

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Problem-Solving Strategy:

Adopt a Different Point of View

Objective To solve problems using the strategy Adopt a Different Point of View

Problem 1:The circle pictured at the right has its center at
the origin and has a radius of 6 units. A point Pis on the circle.
A vertical line passes through Pand intersects the x-axis
at a point A. A horizontal line kalso passes through Pand
intersects the y-axis at point B. What is the distance from
point Ato point B?

9-14

x

B

P

A

k



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Problem-Solving Strategies
1.Guess and Test
2.Organize Data
3.Find a Pattern
4.Make a Drawing
5.Solve a Simpler Problem
6.Reason Logically

7. Adopt a Different Point of View
   8.Account for All Possibilities
   9.Work Backward
   10.Consider Extreme Cases

C

P

x

B

A

k



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Read to understand what is being asked.

List the facts and restate the question.

Facts: A circle has radius 6 units and its

center at the origin.

A vertical line intersects the circle at

point Pand the x-axis at A.

A horizontal line intersects the circle

at point Pand the y-axis at B.

Question:What is the distance from Ato B?

Select a strategy.

If you knew the coordinates of Aand B, you

could solve this problem by using the Pythagorean

Theorem. Unfortunately, however, this information

has not been given. The problem becomes easier if

you use the strategy Adopt a Different Point of View.

Apply the strategy.

If Cis the center of the circle, then polygon CAPB

is a rectangle, and ABis a diagonal of this rectangle.

However,CPis the other diagonal of this same

rectangle. Since the diagonals of a rectangle are

congruent, thenCPhas exactly the same length

as AB.

It is clear from the drawing thatCPis a radius of

the circle. Therefore, its length must be 6 units.

So the length ofAB, which is the distance from

Ato B, is also 6 units.

Check to make sure your answer makes sense.

There is no question that the length ofABis

that of the radius of this circle, or 6 units.

This fact was merely hidden until the problem

was looked at from a different point of view.