Question

namefind distance on the coordinate planelesson 11.3more practice/homeworkonlinevideo tutorials andinteractiveexamples1. on the coordinate plane provided, each unit represents 20 miles.use the coordinate plane to find how far apart two airports arefrom each other.a. plot and label the points to represent thelocations of airport a(125, -325) andairport b(125, 125). then connect thepoints.b. what is the distance between airport aand the x-axis in units and in miles?c. what is the distance between airport band the x-axis in units and in miles?d. what is the distance between the twoairports in miles?2. what are the coordinates of point z(-3.9, -9.3)after a reflection across the y-axis?math on the spot for problems 3-4, find thedistance between the points.3.4.5. use structure find the distance between points d(-5, -3) and e(9, -3)without graphing. how did you find the distance?module 11 • lesson 3 363

Explanation:

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Problem 1

Part B: Distance from A to x-axis

Step1: Identify y-coordinate of A

Airport A: $(125, -325)$, $y=-325$

Step2: Calculate absolute value (units)

$\vert -325 \vert = 325$ units

Step3: Convert to miles (1 unit=20 mi)

$325 \times 20 = 6500$ miles

Part C: Distance from B to x-axis

Step1: Identify y-coordinate of B

Airport B: $(125, 125)$, $y=125$

Step2: Calculate absolute value (units)

$\vert 125 \vert = 125$ units

Step3: Convert to miles

$125 \times 20 = 2500$ miles

Part D: Distance between A and B

Step1: Find vertical distance (units)

$\vert -325 - 125 \vert = \vert -450 \vert = 450$ units

Step2: Convert to miles

$450 \times 20 = 9000$ miles

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Problem 2

Step1: Apply y-axis reflection rule

Rule: $(x,y) \to (-x,y)$

Step2: Substitute point Z

$Z(-3.9, -9.3) \to (3.9, -9.3)$

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Problem 3

Step1: Identify coordinates of F, G

$F(-4, 3)$, $G(3, 3)$

Step2: Calculate horizontal distance

$\vert -4 - 3 \vert = \vert -7 \vert = 7$ units

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Problem 4

Step1: Identify coordinates of J, K

$J(-2, -3)$, $K(-3, -6)$

Step2: Use distance formula

$\sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}$

Step3: Substitute values

$\sqrt{(-3 - (-2))^2 + (-6 - (-3))^2} = \sqrt{(-1)^2 + (-3)^2} = \sqrt{1 + 9} = \sqrt{10}$

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Problem 5

Step1: Recognize horizontal line (same y)

$D(-5, -3)$, $E(9, -3)$, $y=-3$ for both

Step2: Calculate horizontal distance

$\vert 9 - (-5) \vert = \vert 14 \vert = 14$ units

Answer:

1. B. 325 units, 6500 miles

C. 125 units, 2500 miles
D. 9000 miles

1. $(3.9, -9.3)$
2. 7
3. $\sqrt{10}$
4. 14; Since the points share the same y-coordinate, subtract the x-coordinates and take the absolute value.