Use the Pythagorean Theorem to find the distance between points P and Q to the nearest tenth.
Label the length, in units, of each leg of the right triangle.
c² = _____² + _____²
c² = _____ + _____
c = √_____
The distance between point P and point Q is _____ units.
To find the distance between points P and Q using the Pythagorean Theorem, we first need to identify the coordinates of points P and Q. Let’s assume point P has coordinates ((x_1, y_1)) and point Q has coordinates ((x_2, y_2)).
Step 1: Calculate the lengths of the legs of the triangle.
The length of one leg (let’s call it (a)) is the difference in the x-coordinates:
(a = |x_2 – x_1|)
The length of the other leg (let’s call it (b)) is the difference in the y-coordinates:
(b = |y_2 – y_1|)
Step 2: Apply the Pythagorean Theorem.
The Pythagorean Theorem states:
[c^2 = a^2 + b^2]
Step 3: Substitute the values into the formula.
Thus, you would write:
[
c^2 = (|x_2 – x_1|)^2 + (|y_2 – y_1|)^2
]
Step 4: Solve for (c).
To find (c), which is the distance between points P and Q:
[
c = sqrt{(|x_2 – x_1|)^2 + (|y_2 – y_1|)^2}
]
Step