Midpoint and Distance Formulas

If the distance between two points is 10 and one point is (0, 0), what could be the coordinates of the other point?

• (10, 0)

• (5, 5)

• (0, 10)

• (-10, 0)

What is the midpoint of the points (1, 2) and (3, 4)?

• (2, 3)

• (1, 2)

• (3, 4)

• (4, 5)

What is the significance of the distance formula in geometry?

• It calculates the area of a triangle in a coordinate plane.

• It determines the slope of a line between two points.

• It calculates the length of a line segment between two points in a coordinate plane.

• It finds the midpoint of a line segment in a coordinate plane.

What is the distance formula?

• @@d = \sqrt{(x_{2} - x_{1})^2 + (y_{2} - y_{1})^2}@@

• @@d = (x_{2} - x_{1}) + (y_{2} - y_{1})@@

• @@d = \frac{(y_{2} - y_{1})}{(x_{2} - x_{1})}@@

• @@d = \sqrt{(x_{2} + x_{1})^2 + (y_{2} + y_{1})^2}@@

What is the distance between the points (4, 3) and (0, 6)?

• 3

• 4

• 5

• 6

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

• M = \left(\frac{x_{1} + x_{2}}{2}, \frac{y_{1} + y_{2}}{2}\right)

• M = (x_1 + x_2, y_1 + y_2)

• M = \left(\frac{x_{1} - x_{2}}{2}, \frac{y_{1} - y_{2}}{2}\right)

• M = \left(\frac{x_{1} + 2x_{2}}{3}, \frac{y_{1} + 2y_{2}}{3}\right)

What is the relationship between the distance formula and the coordinate plane?

• The distance formula allows us to measure the straight-line distance between any two points in the Cartesian coordinate plane.

• The distance formula is used to calculate the area of a triangle in the coordinate plane.

• The distance formula is only applicable in three-dimensional space.

• The distance formula helps in finding the midpoint of a line segment in the coordinate plane.

How do you derive the distance formula from the Pythagorean theorem?

• By applying the Pythagorean theorem to the right triangle formed by the horizontal and vertical distances between two points.

• By calculating the average of the horizontal and vertical distances between two points.

• By using the formula for the area of a triangle formed by the two points.

• By subtracting the vertical distance from the horizontal distance between two points.

Calculate the distance between the points (1, 1) and (4, 5).

• 3

• 4

• 5

• 6

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}@@