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

Step 1. Plot the points

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

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

Step 3. Use Pythagorean Theorem

Use the Pythagorean Theorem, $a^{2} + b^{2} = c^{2}$ , to find $d$ , the distance between the two points.

On substituting $6$ for $a$ , $8$ for $b$ , and $d$ for $c$ we get

$\begin{array}{rcl} 6^{2} + 8^{2} & = & d^{2} \\ 36 + 64 & = & d^{2} \\ 100 & = & d^{2} \end{array}$

Step 4. Solve for d

As $d^{2} = 100$ , so using the square root property we get

$d = \pm \sqrt{100} d = \pm 10$

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

Short Answer

Step by step solution

Step 1. Plot the points

Step 2. Find the lengths

Step 3. Use Pythagorean Theorem

Step 4. Solve for d

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

Short Answer

Step by step solution

Step 1. Plot the points

Step 2. Find the lengths

Step 3. Use Pythagorean Theorem

Step 4. Solve for d

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Probability and Statistics

Decision Maths

Applied Mathematics

Pure Maths

Discrete Mathematics

Theoretical and Mathematical Physics

Study anywhere. Anytime. Across all devices.

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