Final answer:
The distance AB, given the points A (-4,1) and B (3,-1), is approximately 7.28 units. The distance EF, given the points E (-7,-2) and F (11,3), is approximately 18.68 units.
Step-by-step explanation:
To find the distance between points A and B, where A is given by coordinates A (-4,1) and B is at (3,-1), we use the distance formula: distance AB = √[(x2-x1)^2 + (y2-y1)^2]. The same formula applies to finding distance EF for points E (-7,-2) and F (11,3).
For AB: distance AB = √[(3-(-4))^2 + ((-1)-1)^2] = √[(3+4)^2 + (-2)^2] = √[49 + 4] = √[53] ≈ 7.28 units.
For EF: distance EF = √[(11-(-7))^2 + (3-(-2))^2] = √[(11+7)^2 + (3+2)^2] = √[324 + 25] = √[349] ≈ 18.68 units.
Therefore, the distance AB is approximately 7.28 units and the distance EF is approximately 18.68 units.