Q56. Find the distance between points... [FREE SOLUTION]

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Algebra 1

Carter, Cuevas, Day, Holiday, Luchin

$Math Studyset 91影视 Explanations$ Math

Student Edition 路 801 pages

ISBN: 9780078884801

Chapter 10: Q56. (page 659)

Find the distance between points with the given coordinates and the midpoint of the segment with the given endpoints. Round to the nearest hundredth if necessary.
$(1, 5), (鈭� 4, 鈭� 5)$

Short Answer

Expert verified

The distance between the points $(1, 5)$ and $(鈭� 4, 鈭� 5)$ is $11.18$ .

The midpoint of the line segment with the endpoints at $(1, 5)$ and $(鈭� 4, 鈭� 5)$ is $(鈭� 1.5, 0)$ .

Step by step solution

Step 1. Given.

Coordinates are $(1, 5)$ and $(鈭� 4, 鈭� 5)$

Step 2. Find the distance between the points 1,5 and −4,−5.

The distance (d) between the points $(x_{1}, y_{1})$ and $(x_{2}, y_{2})$ is given by:

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

Therefore, the distance (d) between the points $(1, 5)$ and $(- 4, - 5)$ is:

$d = \sqrt{{(鈭� 4 鈭� 1)}^{2} + {(鈭� 5 鈭� 5)}^{2}} = \sqrt{{(鈭� 5)}^{2} + {(鈭� 10)}^{2}} = \sqrt{5^{2} + 10^{2}} = \sqrt{25 + 100} = \sqrt{125} = \sqrt{25 脳 5} = 5 \sqrt{5} = 5 (2.2361) = 11.1805 鈮� 11.18 (roundedtothenearesthundredth)$

Therefore, the distance (d) between the points $(1, 5)$ and $(- 4, - 5)$ is 11.18.

Step 3. Find the midpoint of the segment with the endpoints at 1,5 and −4,−5.

The midpoint formula states that the midpoint M of a line segment with endpoints at $(x_{1}, y_{1})$ and $(x_{2}, y_{2})$ is given by $M = (\frac{x_{1} + x_{2}}{2}, \frac{y_{1} + y_{2}}{2})$ .

The midpoint (M) of the line segment with endpoints at $(1, 5)$ and $(- 4, - 5)$ is given by:

$M = (\frac{x_{1} + x_{2}}{2}, \frac{y_{1} + y_{2}}{2}) = (\frac{1 + (鈭� 4)}{2}, \frac{5 + (鈭� 5)}{2}) = (\frac{1 鈭� 4}{2}, \frac{5 鈭� 5}{2}) = (\frac{鈭� 3}{2}, \frac{0}{2}) = (鈭� 1.5, 0)$

Therefore, the midpoint of the line segment with the endpoints at $(1, 5)$ and $(- 4, - 5)$ is $(鈭� 1.5, 0)$ .

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91影视

Find the distance between points with the given coordinates and the midpoint of the segment with the given endpoints. Round to the nearest hundredth if necessary.
$(1, 5), (鈭� 4, 鈭� 5)$

Short Answer

Step by step solution

Step 1. Given.

Step 2. Find the distance between the points 1,5 and −4,−5.

Step 3. Find the midpoint of the segment with the endpoints at 1,5 and −4,−5.

One App. One Place for Learning.

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91影视

Find the distance between points with the given coordinates and the midpoint of the segment with the given endpoints. Round to the nearest hundredth if necessary.1,5,鈭�4,鈭�5

Short Answer

Step by step solution

Step 1. Given.

Step 2. Find the distance between the points 1,5 and −4,−5.

Step 3. Find the midpoint of the segment with the endpoints at 1,5 and −4,−5.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Geometry

Decision Maths

Statistics

Discrete Mathematics

Probability and Statistics

Calculus

Study anywhere. Anytime. Across all devices.

Find the distance between points with the given coordinates and the midpoint of the segment with the given endpoints. Round to the nearest hundredth if necessary.
$(1, 5), (鈭� 4, 鈭� 5)$