The distance between two points in a two-dimensional space can be calculated using a couple of formulas, generally depending on the location of those points relative to each other.
To calculate the distance between Point A and Point B, We can simply subtract the y-value of Point B from the y-value of Point A because the x-values of the two points A = (1, 5) and B = (1, 0.4) coincide, they are on the same vertical line. So the formula becomes:
Distance AB = | y1 - y2 |
Distance AB = | 5 - 0.4 | = 4.6 units
For calculating the distance between Point A = (1, 5) and Point C = (-3, 2.5), we have to use the standard distance formula as these points do not align on just one axis. The formula to calculate the distance between any two points (x₁, y₁) and (x₂, y₂) in a two-dimensional Euclidean space is given by
Distance AC = √[((x₂ - x₁)²) + ((y₂ - y₁)²)]
Substituting (1, 5) for (x₁, y₁) and (-3, 2.5) for (x₂, y₂) in the formula, we get:
Distance AC = √[((-3 - 1)²) + ((2.5 - 5)²)]
= √[(-4)² + (-2.5)²]
= √[16 + 6.25]
= √22.25
= 4.72 units
So, the correct option is 'c': Distance AB = 4.6 units, Distance AC = 4.72 units