https://file.aiquickdraw.com/mathbot/file/1726685120875zfbka0pf.jpg

The image you uploaded contains a coordinate grid with points A at (0, 0) and B at (12, 12). You need to find the coordinates of a point that is \( \frac{7}{10} \) of the way from A to B.

This situation involves linear interpolation between two points on a coordinate plane. Given points A at (0, 0) and B at (12, 12), the formula for a point P that lies fraction \( t \) of the way from A to B is given by:

\[ P(x, y) = A + t(B - A) \]

Here \( t = \frac{7}{10} \), and the coordinates for B and A are \( (12, 12) \) and \( (0, 0) \), respectively.

So, the coordinates for P are calculated as:
\[ x = 0 + \frac{7}{10}(12 - 0) \]
\[ y = 0 + \frac{7}{10}(12 - 0) \]

Let's calculate the values of x and y.The coordinates of the point that is \( \frac{7}{10} \) of the way from point A to B are approximately (8.4, 8.4).

Would you like any further details on how this was calculated, or do you have any other questions?

Here are some related questions to consider:
1. How would the coordinates change if the point was \( \frac{1}{4} \) of the way from A to B?
2. What would the coordinates be if point B was at (10, 10) instead?
3. How does the distance between two points on a coordinate plane affect the interpolation?
4. Can you explain how to find the distance between two points given their coordinates?
5. What are some real-life applications of finding a point fractionally between two points?

**Tip**: When calculating the coordinates for a point that lies a certain fraction of the way between two points, it's useful to visualize or draw the scenario to better understand the distances and directions involved.

Find the coordinates of the point that is 7/10 of the way from point A (0, 0) to point B (12, 12).

Learn how to calculate the coordinates of a point that is 7/10 of the way between two points A(0, 0) and B(12, 12) on a coordinate grid using linear interpolation. The key formula used is P(x, y) = A + t(B - A). Suitable for Grade 7-8 students.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation