A student places the map of a city on a coordinate grid and finds that the post office is located at point (-4,3), and the city mall is located at (-9,15). If one unit on the grid is equivalent to 0.5 kilometers, how far is the post office from the city mall



To find the distance between the post office and the city mall, we can use the distance formula:

\[
d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}
\]

where \((x_1, y_1)\) are the coordinates of the post office, and \((x_2, y_2)\) are the coordinates of the city mall.

Given:
- Post office at \((-4, 3)\)
- City mall at \((-9, 15)\)

Substituting these values into the formula:

\[
d = \sqrt{(-9 - (-4))^2 + (15 - 3)^2}
\]

\[
d = \sqrt{(-9 + 4)^2 + (15 - 3)^2}
\]

\[
d = \sqrt{(-5)^2 + (12)^2}
\]

\[
d = \sqrt{25 + 144}
\]

\[
d = \sqrt{169}
\]

\[
d = 13
\]

Since one unit on the grid is equivalent to 0.5 kilometers, the actual distance between the post office and the city mall is:

\[
\text{Distance} = 13 \times 0.5 = 6.5 \text{ kilometers}
\]

So, the post office is 6.5 kilometers from the city mall.

Would you like more details or have any other questions? Here are some related questions you might find interesting:

1. How do you calculate the midpoint between two points on a coordinate grid?
2. What is the equation of the line passing through the post office and city mall?
3. How would the distance change if the scale of the map was different?
4. Can you find the distance between two points without using the distance formula?
5. How do transformations (like translations) affect distances between points on a coordinate grid?

**Tip:** When working with coordinate grids and real-world distances, always ensure that you correctly apply the scale factor to convert between units on the grid and actual distances.

A student places the map of a city on a coordinate grid and finds that the post office is located at point (-4,3), and the city mall is located at (-9,15). If one unit on the grid is equivalent to 0.5 kilometers, how far is the post office from the city mall?

Discover how to calculate the distance between the post office and the city mall using the distance formula on a coordinate grid. Learn about key concepts like coordinate geometry and scale conversion, with a practical example involving a city map. Suitable for students in Grades 7-10.

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