Question

Find the distance between each pair of points.

a) √170 , √106,√10
b) √65,√185,√10
c) √72,√170,√5
d) √81, √162 ,√13

Answer 1

The correct match between the sets of distances and the options is:

a) √170, √106, √10 corresponds to option c).

Step-by-step explanation:

To find the distance between two points x₁, y₁ and x₂, y₂ in a Cartesian plane, we use the distance formula:

`\[ d = √((x_2 - x_1)^2 + (y_2 - y_1)^2) \]`

For example, for the set √72, √170, √5, we can consider three points (0, √5), (√5, 0), and (√13, √12). The distances between these points are:

`\[ d_1 = √((√5 - 0)^2 + (0 - √5)^2) = √10 \]\[ d_2 = √((√13 - √5)^2 + (√12 - 0)^2) = √170 \]\[ d_3 = √((√13 - 0)^2 + (√12 - √5)^2) = √72 \]`

Comparing these values with the provided options, we find that option c) √72, √170, √5 is the correct match.

It's essential to apply the distance formula systematically for each set of points to accurately match them with the given options. The correct answer ensures that the distances are correctly calculated between the specified points.