Questions: Find the distance between the points (3,4) and (-8,4)

Transcript text: Find the distance between the points $(3,4)$ and $(-8,4)$

Solution

Step 1: Identify the coordinates of the points

The given points are $ (3, 4) $ and $ (-8, 4) $.

Step 2: Use the distance formula

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

Step 3: Substitute the values into the formula

Substitute $ (x_1, y_1) = (3, 4) $ and $ (x_2, y_2) = (-8, 4) $ into the formula: \[ d = \sqrt{(-8 - 3)^2 + (4 - 4)^2} \]

Step 4: Simplify the expression

Calculate the differences: \[ d = \sqrt{(-11)^2 + (0)^2} \] \[ d = \sqrt{121 + 0} \] \[ d = \sqrt{121} \]

Step 5: Compute the square root

\[ d = 11 \]

The distance between the points $ (3, 4) $ and $ (-8, 4) $ is $ 11 $.

$\boxed{11}$

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