Find the distance betwen the folowing points.a. Point A(2, 3) and point B(6, 6)b. A = 2 + 3i and B = 6 + 6ic. A = −1 + 5i and B = 5 + 11id. A = 1 − 2i and B = −2 + 3ie. A = 12 − 12 i and B = − 23 + 13 i
Accepted Solution
A:
Answer:a. 5b. 5c. 6√2d. √34e. 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 [tex]\sqrt{(x1-x2)^{2}+(y1-y2)^{2}}[/tex] .... (1)a. Hence, the distance between points A(2,3) and point B(6,6) is [tex]\sqrt{(2-6)^{2}+(3-6)^{2}}=5[/tex] 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 [tex]\sqrt{(2-6)^{2}+(3-6)^{2}}=5[/tex] 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 [tex]\sqrt{(-1-5)^{2}+(5-11)^{2}}=6\sqrt{2}[/tex] 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 [tex]\sqrt{(1+2)^{2}+(-2-3)^{2}}=(34)^{\frac{1}{2}}[/tex] 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 [tex]\sqrt{(12+23)^{2}+(-12-13)^{2}}=43[/tex] units. (Approximate) (Answer)