Find the distance between the points (0, 0) and (x, y) where x = 6 and y = 8.

₹0.0

Question: Find the distance between the points (0, 0) and (x, y) where x = 6 and y = 8.

Options:

Correct Answer: 10

Solution:

Using the distance formula: d = √[(6 - 0)² + (8 - 0)²] = √[36 + 64] = √100 = 10.

Find the distance between the points (0, 0) and (x, y) where x = 6 and y = 8.

Find the distance between the points (0, 0) and (x, y) where x = 6 and y = 8.

Step 1: Identify the coordinates of the two points. The first point is (0, 0) and the second point is (x, y) where x = 6 and y = 8.
Step 2: Write down the distance formula. The distance d between two points (x1, y1) and (x2, y2) is given by d = √[(x2 - x1)² + (y2 - y1)²].
Step 3: Substitute the coordinates into the distance formula. Here, (x1, y1) = (0, 0) and (x2, y2) = (6, 8). So, d = √[(6 - 0)² + (8 - 0)²].
Step 4: Calculate the differences. This gives us d = √[(6)² + (8)²].
Step 5: Calculate the squares. (6)² = 36 and (8)² = 64. So, d = √[36 + 64].
Step 6: Add the squares together. 36 + 64 = 100. So, d = √100.
Step 7: Calculate the square root. √100 = 10.
Step 8: State the final distance. The distance between the points (0, 0) and (6, 8) is 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 System – Understanding how to plot points and interpret their coordinates in a 2D space.