Final answer:
The distance between the points L(7, -1) and M(-2, 4) is calculated using the distance formula, resulting in the square root of 106, which is an irrational number and can be approximated using a calculator.
Step-by-step explanation:
To find the distance between two points in a coordinate plane, we can use the distance formula which is derived from the Pythagorean Theorem. Specifically, if we have two points L(x1, y1) and M(x2, y2), the distance, d, between them is given by:
d = √[(x2 - x1)² + (y2 - y1)²]
Applying this formula to the points L(7, -1) and M(-2, 4), we need to calculate the difference in the x-coordinates and y-coordinates:
- Δx = x2 - x1 = -2 - 7 = -9
- Δy = y2 - y1 = 4 - (-1) = 5
Now we square each difference and add them:
Δx² + Δy² = (-9)² + (5)² = 81 + 25 = 106
The distance is the square root of this sum, which is:
d = √106
Since 106 is a prime number and cannot be simplified into a perfect square, the distance is simply the square root of 106, which is an irrational number. You can leave it as √106 or use a calculator to find a decimal approximation.