If the coordinates of the vertices of a triangle are (1, 2), (4, 6), and (7, 2),

If the coordinates of the vertices of a triangle are (1, 2), (4, 6), and (7, 2), what is the length of the side opposite to the vertex (4, 6)? (2023)

If the coordinates of the vertices of a triangle are (1, 2), (4, 6), and (7, 2), what is the length of the side opposite to the vertex (4, 6)? (2023)

Step 1: Identify the coordinates of the vertices of the triangle. They are (1, 2), (4, 6), and (7, 2).
Step 2: Determine which vertex we are finding the opposite side for. We are looking for the side opposite to the vertex (4, 6).
Step 3: The opposite side is between the other two vertices, which are (1, 2) and (7, 2).
Step 4: Use the distance formula to find the length of the side between the points (1, 2) and (7, 2). The distance formula is: Length = √[(x2 - x1)² + (y2 - y1)²].
Step 5: Substitute the coordinates into the formula. Here, (x1, y1) = (1, 2) and (x2, y2) = (7, 2).
Step 6: Calculate the differences: (x2 - x1) = (7 - 1) = 6 and (y2 - y1) = (2 - 2) = 0.
Step 7: Plug these values into the formula: Length = √[(6)² + (0)²].
Step 8: Calculate (6)² = 36 and (0)² = 0, so Length = √[36 + 0] = √[36].
Step 9: Finally, calculate the square root: √[36] = 6.

Distance Formula – The distance between two points (x1, y1) and (x2, y2) is calculated using the formula √[(x2 - x1)² + (y2 - y1)²].
Triangle Properties – Understanding the relationship between the vertices of a triangle and the sides opposite to them.