Solve a² + b² = c² for c.
c =
Use coordinates to write an expression for the distance between the two points.
c = √( _____ – _____)² + ( _____ – _____)²
Title: Solving for c in Pythagorean Theorem and Distance Formula between Two Points Question: Solve a² + b² = c² for c. c = Use coordinates to write an expression for the distance between the two points. c = √( _____ – _____)² + ( _____ – _____)².
Share
To solve the equation ( a^2 + b^2 = c^2 ) for ( c ), we can isolate ( c ) by taking the square root of both sides:
[ c = sqrt{a^2 + b^2} ]
Now, for the distance between two points with coordinates ((x_1, y_1)) and ((x_2, y_2)), we use the distance formula, which is derived from the Pythagorean theorem. The expression for the distance ( d ) is:
[ d = sqrt{(x_2 – x_1)^2 + (y_2 – y_1)^2} ]
So, filling in the blanks, we have:
c = √(x₂ – x₁)² + (y₂ – y₁)²
This formula provides an effective way to calculate the distance between two points in a Cartesian plane. If you have more questions or need a more in-depth explanation, feel free to check the extended services page!