Math / Geometry

QuestionWhat is the distance between the bank and Hiroto's house on the map? Enter the distance to the nearest quarter mile. (Each unit represents 1 mile.) $\square$ mile's

Studdy Solution

STEP 1

What is this asking? How far apart are two points on a grid, where each box represents a mile, rounded to the nearest quarter mile? Watch out! Remember to round to the nearest quarter mile, not just the nearest mile!

STEP 2

1. Find the difference in x and y coordinates.
2. Use the Pythagorean theorem.
3. Round to the nearest quarter mile.

STEP 3

Let's locate our points!
The bank is at $(-6, 6)$ and Hiroto's house is at $(3, 3)$ .
We're trying to find the distance between them.

STEP 4

Think of this as a right triangle!
The horizontal distance is the difference in the x-coordinates.
That's $3 - (-6) = 3 + 6 = \mathbf{9}$ miles.

STEP 5

The vertical distance is the difference in the y-coordinates.
That's $6 - 3 = \mathbf{3}$ miles.

STEP 6

Remember the Pythagorean theorem? $a^2 + b^2 = c^2$ .
Here, $a$ and $b$ are the legs of the right triangle (our horizontal and vertical distances), and $c$ is the hypotenuse (the distance we want to find).

STEP 7

Let's plug in our values: $9^2 + 3^2 = c^2$ .
This simplifies to $81 + 9 = c^2$ , so $90 = c^2$ .

STEP 8

To find $c$ , we take the square root of both sides: $\sqrt{90} = c$ .
This gives us $c \approx \mathbf{9.4868}$ miles.

STEP 9

We need to round $\mathbf{9.4868}$ to the nearest quarter mile.
Think of quarter miles as $0.25, 0.50, 0.75$ , and $1.00$ .

STEP 10

Is $\mathbf{9.4868}$ closer to $9.50$ or $9.25$ ?
It's closer to $9.50$ !
So, our rounded distance is $\mathbf{9.5}$ miles.

STEP 11

The distance between the bank and Hiroto's house on the map is approximately $\mathbf{9.5}$ miles.

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QuestionWhat is the distance between the bank and Hiroto's house on the map? Enter the distance to the nearest quarter mile. (Each unit represents 1 mile.) $\square$ mile's

Studdy Solution

STEP 1

What is this asking? How far apart are two points on a grid, where each box represents a mile, rounded to the nearest quarter mile? Watch out! Remember to round to the nearest quarter mile, not just the nearest mile!

STEP 2

1. Find the difference in x and y coordinates.
2. Use the Pythagorean theorem.
3. Round to the nearest quarter mile.

STEP 3

Let's locate our points!
The bank is at $(-6, 6)$ and Hiroto's house is at $(3, 3)$ .
We're trying to find the distance between them.

STEP 4

Think of this as a right triangle!
The horizontal distance is the difference in the x-coordinates.
That's $3 - (-6) = 3 + 6 = \mathbf{9}$ miles.

STEP 5

The vertical distance is the difference in the y-coordinates.
That's $6 - 3 = \mathbf{3}$ miles.

STEP 6

Remember the Pythagorean theorem? $a^2 + b^2 = c^2$ .
Here, $a$ and $b$ are the legs of the right triangle (our horizontal and vertical distances), and $c$ is the hypotenuse (the distance we want to find).

STEP 7

Let's plug in our values: $9^2 + 3^2 = c^2$ .
This simplifies to $81 + 9 = c^2$ , so $90 = c^2$ .

STEP 8

To find $c$ , we take the square root of both sides: $\sqrt{90} = c$ .
This gives us $c \approx \mathbf{9.4868}$ miles.

STEP 9

We need to round $\mathbf{9.4868}$ to the nearest quarter mile.
Think of quarter miles as $0.25, 0.50, 0.75$ , and $1.00$ .

STEP 10

Is $\mathbf{9.4868}$ closer to $9.50$ or $9.25$ ?
It's closer to $9.50$ !
So, our rounded distance is $\mathbf{9.5}$ miles.

STEP 11

The distance between the bank and Hiroto's house on the map is approximately $\mathbf{9.5}$ miles.

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QuestionWhat is the distance between the bank and Hiroto's house on the map? Enter the distance to the nearest quarter mile. (Each unit represents 1 mile.) □\square□ mile's

Studdy Solution

STEP 1

What is this asking? How far apart are two points on a grid, where each box represents a mile, rounded to the nearest quarter mile? Watch out! Remember to round to the nearest quarter mile, not just the nearest mile!

STEP 2

1. Find the difference in x and y coordinates.2. Use the Pythagorean theorem.3. Round to the nearest quarter mile.

STEP 3

Let's **locate** our points!The bank is at (−6,6)(-6, 6)(−6,6) and Hiroto's house is at (3,3)(3, 3)(3,3).We're trying to find the distance between them.

STEP 4

Think of this as a right triangle!The horizontal distance is the difference in the x-coordinates.That's 3−(−6)=3+6=93 - (-6) = 3 + 6 = \mathbf{9}3−(−6)=3+6=9 miles.

STEP 5

The vertical distance is the difference in the y-coordinates.That's 6−3=36 - 3 = \mathbf{3}6−3=3 miles.

STEP 6

Remember the Pythagorean theorem? a2+b2=c2a^2 + b^2 = c^2a2+b2=c2.Here, aaa and bbb are the legs of the right triangle (our horizontal and vertical distances), and ccc is the hypotenuse (the distance we want to find).

STEP 7

Let's plug in our values: 92+32=c29^2 + 3^2 = c^292+32=c2.This simplifies to 81+9=c281 + 9 = c^281+9=c2, so 90=c290 = c^290=c2.

STEP 8

To find ccc, we take the square root of both sides: 90=c\sqrt{90} = c90​=c.This gives us c≈9.4868c \approx \mathbf{9.4868}c≈9.4868 miles.

STEP 9

We need to round 9.4868\mathbf{9.4868}9.4868 to the nearest quarter mile.Think of quarter miles as 0.25,0.50,0.750.25, 0.50, 0.750.25,0.50,0.75, and 1.001.001.00.

STEP 10

Is 9.4868\mathbf{9.4868}9.4868 closer to 9.509.509.50 or 9.259.259.25?It's closer to 9.509.509.50!So, our rounded distance is 9.5\mathbf{9.5}9.5 miles.

STEP 11

The distance between the bank and Hiroto's house on the map is approximately 9.5\mathbf{9.5}9.5 miles.

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Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

QuestionWhat is the distance between the bank and Hiroto's house on the map? Enter the distance to the nearest quarter mile. (Each unit represents 1 mile.) $\square$ mile's

1. Find the difference in x and y coordinates.
2. Use the Pythagorean theorem.
3. Round to the nearest quarter mile.

Let's locate our points!
The bank is at $(-6, 6)$ and Hiroto's house is at $(3, 3)$ .
We're trying to find the distance between them.

Think of this as a right triangle!
The horizontal distance is the difference in the x-coordinates.
That's $3 - (-6) = 3 + 6 = \mathbf{9}$ miles.

The vertical distance is the difference in the y-coordinates.
That's $6 - 3 = \mathbf{3}$ miles.

Remember the Pythagorean theorem? $a^2 + b^2 = c^2$ .
Here, $a$ and $b$ are the legs of the right triangle (our horizontal and vertical distances), and $c$ is the hypotenuse (the distance we want to find).

Let's plug in our values: $9^2 + 3^2 = c^2$ .
This simplifies to $81 + 9 = c^2$ , so $90 = c^2$ .

To find $c$ , we take the square root of both sides: $\sqrt{90} = c$ .
This gives us $c \approx \mathbf{9.4868}$ miles.

We need to round $\mathbf{9.4868}$ to the nearest quarter mile.
Think of quarter miles as $0.25, 0.50, 0.75$ , and $1.00$ .

Is $\mathbf{9.4868}$ closer to $9.50$ or $9.25$ ?
It's closer to $9.50$ !
So, our rounded distance is $\mathbf{9.5}$ miles.

The distance between the bank and Hiroto's house on the map is approximately $\mathbf{9.5}$ miles.