find the distanced(p_1&P_2) between points P_1 and P_2. P_1=(4,-5) and P_2=(3,4)
plz show work
Sure! To find the distance between two points (P₁ and P₂) in a coordinate plane, you can use the distance formula:
d = sqrt((x₂ - x₁)² + (y₂ - y₁)²)
Here, P₁ has coordinates (x₁, y₁) and P₂ has coordinates (x₂, y₂).
In this case, P₁ is (4, -5) and P₂ is (3, 4).
Let's substitute these values into the formula:
d = sqrt((3 - 4)² + (4 - (-5))²)
= sqrt((-1)² + (4 + 5)²)
= sqrt(1 + 9²)
= sqrt(1 + 81)
= sqrt(82)
Therefore, the distance between P₁ and P₂ is sqrt(82), which is approximately 9.06 units.