find the distance d(P_1 & P_1) between points P_1 and P_2. P_1=(4,-5)and P_2=(3,4)
please show work
(3,4).(4,-5).
D^2 = (4-3)^2 + (-5-4)^2 = 1 + 81 = 82
D = sgrt(82) = 9.06.
To find the distance between two points, you can use the distance formula, which is derived from the Pythagorean theorem. The formula to find the distance between two points (P1 and P2) in a Cartesian coordinate system is:
d(P1, P2) = sqrt((x2 - x1)^2 + (y2 - y1)^2)
Given the points P1(4,-5) and P2(3,4), we can substitute the values into the formula:
d(P1, P2) = sqrt((3 - 4)^2 + (4 - (-5))^2)
= sqrt((-1)^2 + (4 + 5)^2)
= sqrt(1 + 81)
= sqrt(82)
Therefore, the distance between P1 and P2 is sqrt(82) units.