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Chapter 11: Q. 11.1 (page 1071)

Use the rectangular coordinate system to find the distance between the points (6,1) and (2,-2).

Short Answer

Expert verified

The distance between the given points is 5.

Step by step solution

01

Step 1. Plot the points

Plot the two points. Connect the two points with a line and then draw a right triangle.

02

Step 2. Find the lengths

Find the length of each leg.

The rise is three units and the run is four units. So the right triangle can be shown as

03

Step 3. Use Pythagorean Theorem

Use the Pythagorean Theorem, a2+b2=c2, to find d, the distance between the two points.

Substitute 3for a, 4for b, and dfor cwe get

32+42=d29+16=d225=d2

04

Step 4. Solve for d

As d2=25, so using the square root property we get

d=卤25d=卤5

But the value of distance cannot be negative, so we eliminate d=-5.

So the distance between the points is role="math" localid="1645188625093" d=5.

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