Work out the length of line LM. Give your answer to 3 decimal places.

Question image

Understand the Problem

The question asks for the calculation of the length of the line segment joining the points L and M on a Cartesian plane. This involves using the distance formula to find the length based on the coordinates provided.

Answer

The length of line \(LM\) is approximately $6.403$.
Answer for screen readers

The length of line (LM) is approximately $6.403$.

Steps to Solve

  1. Identify the coordinates of points L and M

The coordinates are given as follows:

  • Point L: $(-3, 2)$
  • Point M: $(1, -3)$
  1. Use the distance formula

The distance (d) between two points ((x_1, y_1)) and ((x_2, y_2)) is calculated using the formula:

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

  1. Plug in the coordinates into the formula

Substituting the coordinates for L and M into the formula:

  • For L: ( x_1 = -3, y_1 = 2 )
  • For M: ( x_2 = 1, y_2 = -3 )

This gives:

$$ d = \sqrt{(1 - (-3))^2 + (-3 - 2)^2} $$

  1. Calculate the differences

Calculate (x_2 - x_1) and (y_2 - y_1):

  • ( x_2 - x_1 = 1 + 3 = 4 )
  • ( y_2 - y_1 = -3 - 2 = -5 )
  1. Substitute the differences back into the distance formula

Now, substitute these differences back into the formula:

$$ d = \sqrt{(4)^2 + (-5)^2} $$

  1. Calculate the squares and sum them

Calculating the squares:

$$ d = \sqrt{16 + 25} $$

$$ d = \sqrt{41} $$

  1. Calculate the square root

Now we find the square root:

$$ d \approx 6.403 $$

  1. Round to three decimal places

Therefore, rounding to three decimal places gives:

$$ d \approx 6.403 $$

The length of line (LM) is approximately $6.403$.

More Information

The distance formula is derived from the Pythagorean theorem, relating the lengths of the sides of a right triangle. The result tells us how far apart the two points are on the Cartesian plane.

Tips

  • Not squaring the differences correctly.
  • Forgetting to apply the square root at the end.
  • Miscalculating the coordinates, leading to incorrect input in the formula.

AI-generated content may contain errors. Please verify critical information

Thank you for voting!
Use Quizgecko on...
Browser
Browser