A(-1,-2) B(7,2)
show that the lenght AB may be written in the form p root5 wjere p is an integer to be found??
is then ans just 4root5??
if not hep please thenks
To find the length AB between points A(-1, -2) and B(7, 2), we can use the distance formula.
The distance formula states that the distance between two points (x₁, y₁) and (x₂, y₂) in a coordinate plane is given by:
d = √((x₂ - x₁)² + (y₂ - y₁)²)
In this case, the coordinates of A are (-1, -2) and the coordinates of B are (7, 2).
So, substituting the values into the formula, we get:
d = √((7 - (-1))² + (2 - (-2))²)
= √((7 + 1)² + (2 + 2)²)
= √(8² + 4²)
= √(64 + 16)
= √80
Now, we need to simplify √80.
First, we can factorize 80.
80 = 2² * 2 * 2 * 5
Taking out each perfect square factor, we have:
√80 = √(2² * 2 * 2 * 5)
= 2 * √(2 * 2 * 5)
= 2 * 2 * √5
= 4√5
Therefore, the length AB can be expressed as 4√5.