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Chapter 11: Q. 11.2 (page 1071)

Use the rectangular coordinate system to find the distance between the points (5,3) and (-3,-3).

Short Answer

Expert verified

The distance between the given points is 10.

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 six units and the run is eight 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.

On substituting 6for a, 8for b, and dfor cwe get

62+82=d236+64=d2100=d2

04

Step 4. Solve for d 

As d2=100, so using the square root property we get

d=卤100d=卤10

But the value of distance cannot be negative, so we eliminate d=-10.

So the distance between the points is d=10.

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