Question

Find the distance between the points (-4, 5) and (2, -3).

Hint:

The order of subtraction doesn't matter because the difference is squared, making the result always non-negative.

Answer 1

Step 1: Write the distance formula.
To find the distance between two points in a coordinate plane, we use the distance formula:
\( d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \)
This formula is derived from the Pythagoras theorem and helps calculate the straight-line distance between two points.

Step 2: Identify the coordinates of the given points.
The given points are:
First point \(A(-4, 5)\) → \(x_1 = -4\), \(y_1 = 5\)
Second point \(B(2, -3)\) → \(x_2 = 2\), \(y_2 = -3\)

Step 3: Substitute the values into the distance formula.
\( d = \sqrt{(2 - (-4))^2 + (-3 - 5)^2} \)

Step 4: Simplify the expression.
First simplify inside the brackets:
\(2 - (-4) = 6\)
\(-3 - 5 = -8\)

Now square the values:
\(6^2 = 36\)
\((-8)^2 = 64\)

Add them together:
\(36 + 64 = 100\)

Step 5: Find the square root.
\( d = \sqrt{100} \)
\( d = 10 \)

Final Answer:
The distance between the points (-4, 5) and (2, -3) is 10 units.