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

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

Options:

Correct Answer: 7

Solution:

Using the distance formula: d = √[(4 - (-2))² + (5 - (-3))²] = √[(4 + 2)² + (5 + 3)²] = √[36 + 64] = √100 = 10.

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

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

Step 1: Identify the coordinates of the two points. The first point is (-2, -3) and the second point is (4, 5).
Step 2: Write down the distance formula: d = √[(x2 - x1)² + (y2 - y1)²].
Step 3: Assign the coordinates to the formula. Here, x1 = -2, y1 = -3, x2 = 4, and y2 = 5.
Step 4: Substitute the values into the formula: d = √[(4 - (-2))² + (5 - (-3))²].
Step 5: Simplify the expressions inside the parentheses: d = √[(4 + 2)² + (5 + 3)²].
Step 6: Calculate the values: d = √[6² + 8²].
Step 7: Find the squares: d = √[36 + 64].
Step 8: Add the results: d = √100.
Step 9: Take the square root: d = 10.

Distance Formula – The distance between two points in a Cartesian plane is calculated using the formula d = √[(x2 - x1)² + (y2 - y1)²].
Coordinate Geometry – Understanding how to plot points and calculate distances in a two-dimensional space.