To find the distance between the two points on the coordinate plane, we can use the Pythagorean theorem. Here’s how we do it step by step:
Step 1: Identify the coordinates of the points
The points are:
- Point 1: (0, 0)
- Point 2: (3, 4)
Step 2: Calculate the differences in the x-coordinates and y-coordinates
- The difference in the x-coordinates (horizontal leg) is \(3 - 0 = 3\).
- The difference in the y-coordinates (vertical leg) is \(4 - 0 = 4\).
Step 3: Use the Pythagorean theorem
The Pythagorean theorem states that for a right triangle, \(a^2 + b^2 = c^2\), where \(a\) and \(b\) are the lengths of the legs, and \(c\) is the length of the hypotenuse.
In our case:
- \(a = 3\)
- \(b = 4\)
So, we calculate:
\[ c^2 = 3^2 + 4^2 \]
\[ c^2 = 9 + 16 \]
\[ c^2 = 25 \]
\[ c = \sqrt{25} \]
\[ c = 5 \]
Step 4: Verify the answer
We can check our answer by ensuring that the calculations are correct:
- \(3^2 = 9\)
- \(4^2 = 16\)
- \(9 + 16 = 25\)
- \(\sqrt{25} = 5\)
The calculations are correct, so the distance between the points (0, 0) and (3, 4) is 5 units.
Final Answer: 5
Parent Tip: Review the logic above to help your child master the concept of pythagorean theorem on coordinate plane worksheet.
