Questions: Calculate the distance between the points L=(-3,-4) and F=(1,1) in the coordinate plane. Give an exact answer (not a decimal approximation). Distance:

Calculate the distance between the points L=(-3,-4) and F=(1,1) in the coordinate plane.
Give an exact answer (not a decimal approximation).

Distance:

Transcript text: Calculate the distance between the points $L=(-3,-4)$ and $F=(1,1)$ in the coordinate plane. Give an exact answer (not a decimal approximation). Distance: $\square$

Solution

Solution Steps

Step 1: Identify the coordinates of the points

The coordinates of point $ L $ are $ (-3, -4) $ and the coordinates of point $ F $ are $ (1, 1) $.

Step 2: Use the distance formula

The distance $ d $ between two points $(x_1, y_1)$ and $(x_2, y_2)$ in the coordinate plane is given by: \[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \]

Step 3: Substitute the coordinates into the distance formula

Substitute $ x_1 = -3 $, $ y_1 = -4 $, $ x_2 = 1 $, and $ y_2 = 1 $ into the formula: \[ d = \sqrt{(1 - (-3))^2 + (1 - (-4))^2} \] \[ d = \sqrt{(1 + 3)^2 + (1 + 4)^2} \] \[ d = \sqrt{4^2 + 5^2} \] \[ d = \sqrt{16 + 25} \] \[ d = \sqrt{41} \]