Find the distance betwen the folowing points.
a. point a(2, 3) and point b(6, 6)
b. a = 2 + 3i and b = 6 + 6i
c. a = −1 + 5i and b = 5 + 11i
d. a = 1 − 2i and b = −2 + 3i
e. a = 1
2 − 1
2 i and b = − 2
3 + 1
3 i

a. 5

b. 5

c. 6√2

d. √34

e. 43 (appx.)

Step-by-step explanation:

The distance between two points on the coordinate plane having coordinate (x1, y1) and (x2, y2) is given by .... (1)

a. Hence, the distance between points A(2,3) and point B(6,6) is units. {Using equation (1)}

b. Coordinates of A and B in the Cartesian coordinate plane are (2,3) and (6,6) respectively.

Hence, the distance between A and B is units.

c. Coordinates of A and B in the Cartesian coordinate plane are (-1,5) and (5,11) respectively.

Hence, the distance between A and B is units.

d. Coordinates of A and B in the Cartesian coordinate plane are (1,-2) and (-2,3) respectively.

Hence, the distance between A and B is units.

e. Coordinates of A and B in the Cartesian coordinate plane are (12,-12) and (-23,13) respectively.

Hence, the distance between A and B is units. (Approximate) (Answer)

a_n = a_1 + (n - 1)d

the first term is 6.

the common difference d = ?

when you find d, replace n with 7 and d with the common difference to find your answer.

answer: $13,622.84

step-by-step explanation: check the picture for info and stats : )