Remember to find the length of a diagonal side or line, you can use the distance formula: d = √((x2 - x1)² + (y2 - y1)²)
Understand the Problem
The question presents a mathematical formula for calculating the length of a diagonal side or line using the distance formula based on the coordinates of two points.
Answer
The length of the diagonal is \( d = 5 \).
Answer for screen readers
The length of the diagonal side is ( d = 5 ).
Steps to Solve
- Identify the coordinates of the two points
Let's say we have two points, ( A(x_1, y_1) ) and ( B(x_2, y_2) ). For instance, let ( A(2, 3) ) and ( B(5, 7) ).
- Plug the coordinates into the distance formula
Using the distance formula:
$$ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} $$
we substitute the coordinates of points ( A ) and ( B ):
$$ d = \sqrt{(5 - 2)^2 + (7 - 3)^2} $$
- Calculate the differences
Calculate the differences:
$$ x_2 - x_1 = 5 - 2 = 3 $$ $$ y_2 - y_1 = 7 - 3 = 4 $$
- Square the differences
Now, square those differences:
$$ d = \sqrt{(3)^2 + (4)^2} $$
- Calculate the squares and sum them
Compute the squares:
$$ d = \sqrt{9 + 16} $$
- Take the square root
Finally, take the square root of the sum:
$$ d = \sqrt{25} = 5 $$
The length of the diagonal side is ( d = 5 ).
More Information
The distance formula is derived from the Pythagorean theorem, which relates the lengths of the sides of a right triangle. It allows us to find the distance between two points in a coordinate plane.
Tips
- Forgetting to square the differences before summing them.
- Neglecting to take the square root at the end of the calculation.
- Mixing up ( x_1 ) and ( x_2 ) or ( y_1 ) and ( y_2 ) when substituting.
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