Example 2Using the Distance FormulaBird Watching A bird watcheruses a grid to photograph andrecord the locations of birdsfeeding on the ground. The grid ismade of fishing net with strandsthat are 1 foot apart. In the gridshown, each point represents thelocation of a bird. How far apartare the birds at points A and B?yIC6.4.32D1 2 3 4567 8 9SolutionThe coordinates of point A are (3, 2). The coordinates of point B are(7, 5).V(x,- x,² + ( - y,)²= V(7 – 3)2 + (5 – 2)?d =Distance formulaSubstitute 7 for x,, 3 for X,,5 for y,, and 2 for y,.%3D=DV4? + 32Subtract.%3D= V16 + 9Evaluate powers.= V25Add.= 5Simplify.Answer The birds at points A and B are 5 feet apart.Guided Practice for Example #23) In the above example, how far apart are the birds at point C and point D?

Example 2 Using the Distance Formula Bird Watching A bird watcher uses a grid to photograph and record the locations of birds feeding on the ground. The grid is made of fishing net with strands that are 1 foot apart. In the grid shown, each point represents the location of a bird. How far apart are the birds at points A and B? y 7. C 6. B 3 20 [A O 1 2 3 4 5 6 7 8 9 Solution The coordinates of point A are (3, 2). The coordinates of point B are (7,5). d = V(x, - x,)² + (y2 – y;)² Distance formula Substitute 7 for x,, 3 for X4, X21 5 for y,, and 2 for y,. = V(7- 3)2 + (5 – 2)? %3D V42 + 32 Subtract. = V16 + 9 Evaluate powers. %3D = V25 Add. %3D = 5 Simplify. Answer The birds at points A and B are 5 feet apart. Guided Practice for Example #2 3) In the above example, how far apart are the birds at point C and point D? 4.

Example 2 Using the Distance Formula Bird Watching A bird watcher uses a grid to photograph and record the locations of birds feeding on the ground. The grid is made of fishing net with strands that are 1 foot apart. In the grid shown, each point represents the location of a bird. How far apart are the birds at points A and B? y 7. C 6. B 3 20 [A O 1 2 3 4 5 6 7 8 9 Solution The coordinates of point A are (3, 2). The coordinates of point B are (7,5). d = V(x, - x,)² + (y2 – y;)² Distance formula Substitute 7 for x,, 3 for X4, X21 5 for y,, and 2 for y,. = V(7- 3)2 + (5 – 2)? %3D V42 + 32 Subtract. = V16 + 9 Evaluate powers. %3D = V25 Add. %3D = 5 Simplify. Answer The birds at points A and B are 5 feet apart. Guided Practice for Example #2 3) In the above example, how far apart are the birds at point C and point D? 4.

Elementary Geometry For College Students, 7e

7th Edition

ISBN:9781337614085

Author:Alexander, Daniel C.; Koeberlein, Geralyn M.

Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.

ChapterP: Preliminary Concepts

SectionP.CT: Test

Problem 1CT

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Question

Example 2
Using the Distance Formula
Bird Watching A bird watcher
uses a grid to photograph and
record the locations of birds
feeding on the ground. The grid is
made of fishing net with strands
that are 1 foot apart. In the grid
shown, each point represents the
location of a bird. How far apart
are the birds at points A and B?
y
IC
6.
4.
3
2
D
1 2 3 4
56
7 8 9
Solution
The coordinates of point A are (3, 2). The coordinates of point B are
(7, 5).
V(x,- x,² + ( - y,)²
= V(7 – 3)2 + (5 – 2)?
d =
Distance formula
Substitute 7 for x,, 3 for X,,
5 for y,, and 2 for y,.
%3D
=DV4? + 32
Subtract.
%3D
= V16 + 9
Evaluate powers.
= V25
Add.
= 5
Simplify.
Answer The birds at points A and B are 5 feet apart.
Guided Practice for Example #2
3) In the above example, how far apart are the birds at point C and point D?

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