Question

Find the distance between the points. (Find MZ)

a) ( MZ = √{(x_2 - x_1)^2 + (y_2 - y_1)^2} )

b) ( MZ = |x_2 - x_1| + |y_2 - y_1| )

c) ( MZ = x_2 - x_1 + y_2 - y_1 )

d) ( MZ = frac{x_2 + x_1}{2} + frac{y_2 + y_1}{2} )

Answer 1

To calculate the distance between two points (MZ), the correct formula is MZ = √{(x_2 - x_1)^2 + (y_2 - y_1)^2}. This is option a) and follows from the application of the Pythagorean theorem in a two-dimensional coordinate system.

Step-by-step explanation:

To find MZ, which is the distance between two points in a coordinate system, we need to use the distance formula. The correct formula to calculate this distance is:

MZ = √{(x_2 - x_1)^2 + (y_2 - y_1)^2}

Where (x_1, y_1) and (x_2, y_2) are the coordinates of points M and Z respectively. This is derived from the Pythagorean theorem, which is used to find the length of the hypotenuse of a right triangle. The other options b) and c) do not correctly calculate the distance, and d) seems to be an unrelated equation.

Option a) is the only correct choice as it represents the Pythagorean theorem applied in a two-dimensional space to calculate the straight-line distance between two points.