How would you write that line segment PK has equal length with line segment OQ?
To write the statement "Line segment PK has equal length with line segment OQ," you can use mathematical notation. Here's how you can express it:
|PK| = |OQ|
In this notation, the bars around the line segments symbolize their length or magnitude. The equality sign indicates that both line segments have the same length.
However, it's important to note that as an AI text-based model, I don't have visual context. So, I'll assume you're referring to a standard Cartesian coordinate system. In such a system, the line segment PK is defined by its endpoints P and K, and the line segment OQ is defined by its endpoints O and Q. Both line segments have equal length if the distance between P and K is equal to the distance between O and Q.
To determine whether the line segments have equal length, you'll need to calculate the distances between their respective endpoints. The distance formula in a Cartesian coordinate system is:
Distance = √((x2 - x1)^2 + (y2 - y1)^2)
Substitute the coordinates of the endpoints into the formula to calculate the distances. If the calculated distances are equal, the line segments have the same length.
For example, let's assume P(2, 3), K(5, 7), O(-1, 2), and Q(4, 6). Substitute these coordinates into the distance formula:
|PK| = √((5 - 2)^2 + (7 - 3)^2)
|PK| = √(3^2 + 4^2)
|PK| = √(9 + 16)
|PK| = √25
|PK| = 5
|OQ| = √((4 - (-1))^2 + (6 - 2)^2)
|OQ| = √(5^2 + 4^2)
|OQ| = √(25 + 16)
|OQ| = √41
Since |PK| ≠ |OQ| (5 ≠ √41), the line segments PK and OQ do not have equal length.