3 mistakes learners make with magnitude, each one named and explained.
The magnitude is Pythagoras on the components, and it is never negative.
The magnitude of 6i - 8j is given as -2, the two components combined.
Two numbers and a single answer wanted, and adding is the operation that needs no decision.
Question. 6i - 8j
A common answer. 6 + (-8) = -2
The answer. the root of 36 + 64, which is 10
Why. A magnitude is a length and can never be negative.
A magnitude is always positive. A negative answer means no squaring happened.
The hypotenuse is given as the two shorter sides added together.
The rule is remembered as the two shorter sides make the long one, which is nearly the shape of it.
Question. Legs of 6 cm and 8 cm
A common answer. 6 + 8 = 14
The answer. 10
Why. If the hypotenuse were the sum, the triangle would be a flat line.
The hypotenuse is always shorter than the other two added together. Always.
The squares are added correctly and the total is given as the length.
Reaching 100 feels like arriving, because the hard arithmetic is done.
Question. Legs of 6 and 8
A common answer. 36 + 64 = 100
The answer. the square root of 100, which is 10
Why. 100 is the area of the square on the hypotenuse, not its length.
Pythagoras always ends with a root. If you did not take one, you are not finished.
WAJD spots these patterns in your child's answers and names the one behind their wrong answers, instead of just marking them wrong.