Mrs. Kim's Distance and Midpoint Formulas

What is the midpoint of the points (2, 3) and (4, 7)?

• (3, 5)

• (4, 5)

• (3, 6)

• (2, 5)

What is the formula for the distance between two points in a coordinate plane?

• @@d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}@@

• @@d = |x_2 - x_1| + |y_2 - y_1|@@

• @@d = (x_2 - x_1)(y_2 - y_1)@@

• @@d = \frac{(y_2 - y_1)}{(x_2 - x_1)}@@

How do you find the distance between the points (-1, -1) and (3, 3)?

• @@4\sqrt{2}@@

• @@5@@

• @@6@@

• @@3\sqrt{2}@@

What is the significance of the distance formula in geometry?

• It is used to calculate the area of a triangle.

• It is used to determine the length of a line segment between two points in a coordinate plane.

• It helps in finding the midpoint of a line segment.

• It is used to calculate the slope of a line.

How do you calculate the distance between the points (3, 0) and (5, -2)?

• @@rac{5}{2}@@

• @@rac{3 oot{2}}{2}@@

• @@rac{8}{3}@@

• @@ ext{2.83}@@

What is the distance between the points (1, 1) and (1, -1)?

• 1

• 2

• 3

• 4

What is the formula for calculating the distance between two points in a 3D space?

• @@d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2 + (z_2 - z_1)^2}@@

• @@d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}@@

• @@d = |x_2 - x_1| + |y_2 - y_1| + |z_2 - z_1|@@

• @@d = \sqrt{(x_2 - x_1)^2 + (z_2 - z_1)^2}@@

What is the distance between the points (1, 2) and (4, 6)?

• 3

• 4

• 5

• 6

What is the midpoint formula for finding the midpoint between two points (x1, y1) and (x2, y2)?

• M = \left(\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2}\right)

• M = \left(\frac{x_1 - x_2}{2}, \frac{y_1 - y_2}{2}\right)

• M = \left(\frac{x_1 + x_2}{x_1 - x_2}, \frac{y_1 + y_2}{y_1 - y_2}\right)

• M = \left(\frac{x_1 + 2x_2}{3}, \frac{y_1 + 2y_2}{3}\right)

If the coordinates of two points are (2, 3) and (2, 7), what is the distance between them?

• 2

• 4

• 5

• 6