The Correct Answer and Explanation is:
The correct answer is that the length of the segment WV is √65.
To determine the length of the line segment WV, we must first identify the coordinates of points W and V from the provided graph. The graph is a Cartesian coordinate plane with a grid. By starting at the origin (0,0), we can find the coordinates for each point. For point W, we move 2 units to the left on the x-axis and 3 units down on the y-axis, making its coordinates (-2, -3). For point V, we move 1 unit to the left on the x-axis and 5 units up on the y-axis, so its coordinates are (-1, 5).
With the coordinates identified, we can use the Distance Formula to calculate the length of the segment connecting these two points. The Distance Formula is derived from the Pythagorean theorem and is expressed as d = √[(x₂ – x₁)² + (y₂ – y₁)²].
Let’s assign W as (x₁, y₁) = (-2, -3) and V as (x₂, y₂) = (-1, 5). Now we substitute these values into the formula:
WV = √[(-1 – (-2))² + (5 – (-3))²]
First, we solve the operations inside the parentheses:
-1 – (-2) = -1 + 2 = 1
5 – (-3) = 5 + 3 = 8
Now, we substitute these results back into the formula:
WV = √[(1)² + (8)²]
Next, we square each number:
1² = 1
8² = 64
Finally, we add the results and take the square root:
WV = √[1 + 64]
WV = √65
The number 65 does not have any perfect square factors, so the square root cannot be simplified further. Therefore, the exact length of the segment WV is √65.
