If the coordinates of the vertices of triangle PQR are P(1, 2), Q(4, 6), and R(1

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Question: If the coordinates of the vertices of triangle PQR are P(1, 2), Q(4, 6), and R(1, 6), what is the length of side PQ?

Options:

Correct Answer: 4

Solution:

Using the distance formula, PQ = √((4 - 1)² + (6 - 2)²) = √(9 + 16) = √25 = 5.

If the coordinates of the vertices of triangle PQR are P(1, 2), Q(4, 6), and R(1, 6), what is the length of side PQ?

If the coordinates of the vertices of triangle PQR are P(1, 2), Q(4, 6), and R(1, 6), what is the length of side PQ?

Step 1: Identify the coordinates of points P and Q. P is at (1, 2) and Q is at (4, 6).
Step 2: Use the distance formula to find the length of side PQ. The distance formula is: distance = √((x2 - x1)² + (y2 - y1)²).
Step 3: Substitute the coordinates of P and Q into the formula. Here, x1 = 1, y1 = 2, x2 = 4, and y2 = 6.
Step 4: Calculate the differences: (x2 - x1) = (4 - 1) = 3 and (y2 - y1) = (6 - 2) = 4.
Step 5: Square the differences: (3)² = 9 and (4)² = 16.
Step 6: Add the squared differences: 9 + 16 = 25.
Step 7: Take the square root of the sum: √25 = 5.
Step 8: Conclude that the length of side PQ is 5.

Distance Formula – The distance between two points (x1, y1) and (x2, y2) is calculated using the formula √((x2 - x1)² + (y2 - y1)²).
Coordinate Geometry – Understanding how to plot points and calculate distances in a Cartesian coordinate system.