Solve a² + b² = c² for c.
c =
Use coordinates to write an expression for the distance between the two points.
c = √(_______ – _______)² + (_______ – _______)²
Solve a² + b² = c² for c. c = Use coordinates to write an expression for the distance between the two points. c = √(_______ – _______)² + (_______ – _______)².
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To solve for ( c ) in the equation ( a^2 + b^2 = c^2 ), we can rearrange it:
1. Start with the original equation:
[
a^2 + b^2 = c^2
]
2. To solve for ( c ), take the square root of both sides:
[
c = sqrt{a^2 + b^2}
]
Now, for the distance between two points ((x_1, y_1)) and ((x_2, y_2)), the expression is given by:
[
c = sqrt{(x_2 – x_1)^2 + (y_2 – y_1)^2}
]
So, filling in the blanks in your expression gives:
[
c = sqrt{(x_2 – x_1)^2 + (y_2 – y_1)^2}
]
This formula is derived from the Pythagorean theorem, where the differences in the x-coordinates and y-coordinates represent the legs of a right triangle, and ( c ) represents the length of the hypotenuse (the distance between the two points). If you need further assistance or examples, feel free to ask!