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Geometry

Ray C. Jurgensen, Richard G. Brown, John W. Jurgensen

$Math Studyset Vaia Explanations$ Math

Student Edition · 227 pages

ISBN: 9780395977279

Chapter 13: Q. 10 (page 526)

10. Find the distance between the points named. Give all answers in simplest
form.
(0, 0) and (5, -3).
(3, -2) and (-5, -2).
(4, 4) and (-3, -3).

Short Answer

Expert verified

The distance is $\sqrt{34}$ .
The distance is 8.
The distance is $\sqrt{98}$ .

Step by step solution

a.Step-1 – Given

The given points are (0,0) and (5, -3).

Step-2 – To determine

We have to find the distance between the points.

Step-3 – Calculation

We will use the distance formula

$d = \sqrt{{(x_{2} - x_{1})}^{2} + {(y_{2} - y_{1})}^{2}}$

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Most popular questions from this chapter

In Exercises 16-19 a point P on a line and the slope of the line are given. Sketch the line and find the coordinates of two other points on the line.

P(0, -5); slope = $- \frac{1}{4}$ .

This exercise provides a geometric method of justifying the fact that you can use any two points on a line to determine the slope of the line. Horizontal and vertical segments have been drawn as shown. Supply the reason for each step.

Key steps of proof:

$\begin{array}{l} 1. ∠ B ≅ ∠ A \\ 2. ∠ 1 ≅ ∠ 2 \\ 3. Δ L B N ~ Δ D A J \\ 4. \frac{B N}{A J} = \frac{L B}{D A}, o r \frac{B N}{L B} = \frac{A J}{D A} \end{array}$

5. The slope of LN equals $\frac{B N}{L B}$ and the slope of DJ equals $\frac{A J}{D A}$

6. Slope of LN equals to slope of DJ.

Use the distance formula to find the distance between the two points.

(-8, 6) and (0, 0)

Use the distance formula to find the distance between the two points.

(5, 4) and (1, -2)

A line with slope $- \frac{5}{2}$ passes through points (7, -4) and (?, 6).

See all solutions

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10. Find the distance between the points named. Give all answers in simplest
form.
(0, 0) and (5, -3).
(3, -2) and (-5, -2).
(4, 4) and (-3, -3).

Short Answer

Step by step solution

a.Step-1 – Given

Step-2 – To determine

Step-3 – Calculation

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Most popular questions from this chapter

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10. Find the distance between the points named. Give all answers in simplestform.(0, 0) and (5, -3).(3, -2) and (-5, -2).(4, 4) and (-3, -3).

Short Answer

Step by step solution

a.Step-1 – Given

Step-2 – To determine

Step-3 – Calculation

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Applied Mathematics

Probability and Statistics

Discrete Mathematics

Calculus

Pure Maths

Mechanics Maths

Study anywhere. Anytime. Across all devices.

10. Find the distance between the points named. Give all answers in simplest
form.
(0, 0) and (5, -3).
(3, -2) and (-5, -2).
(4, 4) and (-3, -3).