Question

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

Answer 1

a. 5

b. 5

c. 6√2

d. √34

e. 43 (appx.)

Explanation:

The distance between two points on the coordinate plane having coordinate (x1, y1) and (x2, y2) is given by
`\sqrt{(x1-x2)^(2)+(y1-y2)^(2)}` .... (1)

a. Hence, the distance between points A(2,3) and point B(6,6) is
`\sqrt{(2-6)^(2)+(3-6)^(2)}=5` 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
`\sqrt{(2-6)^(2)+(3-6)^(2)}=5` 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
`\sqrt{(-1-5)^(2)+(5-11)^(2)}=6√(2)` 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
`\sqrt{(1+2)^(2)+(-2-3)^(2)}=(34)^{(1)/(2)}` 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
`\sqrt{(12+23)^(2)+(-12-13)^(2)}=43` units. (Approximate) (Answer)