Exploring Midpoint and Distance in Geometry

What are the main objectives of the lesson on midpoint and distance in the coordinate plane?

• To explore the concept of symmetry

• To develop and apply the midpoint formula and use the distance formula and Pythagorean theorem

• To learn about angles and triangles

• To understand the properties of circles

How do you find the distance between two points on a number line?

• By counting the jumps between the points

• By adding the coordinates of the points

• By finding the difference between the coordinates

• By multiplying the coordinates of the points

What is the midpoint between the ages of 8 and 12?

• 9

• 8

• 11

• 10

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

• The difference of the coordinates divided by 2

• The sum of the coordinates divided by 2

• The product of the coordinates divided by 2

• The average of the x-coordinates and the average of the y-coordinates

If the midpoint of segment XY is (6, 1) and one endpoint X is (2, 7), what are the coordinates of the other endpoint Y?

• (4, 5)

• (8, 3)

• (12, -1)

• (10, -5)

What is the distance formula used to calculate the distance between two points in a coordinate plane?

• The product of the x-coordinates and the y-coordinates

• The sum of the x-coordinates squared plus the sum of the y-coordinates squared

• The difference between the x-coordinates squared plus the difference between the y-coordinates squared, then take the square root

• The average of the x-coordinates and the y-coordinates

What is the distance between points F(1, 2) and G(5, 5) using the distance formula?

• 6 units

• 5 units

• 4 units

• 7 units

How can the Pythagorean theorem be used to find the distance between two points in a coordinate plane?

• By finding the average of the coordinates

• By multiplying the coordinates of the points

• By adding the coordinates of the points

• By turning the segment into a right triangle and using the sum of the squares of the legs

What is the distance of the throw from first base to a point 10 feet from third base on a baseball field with 90-foot sides?

• 110.4 feet

• 120.4 feet

• 130.4 feet

• 100.4 feet

What is the sum of the squares of the lengths of the legs in a right triangle equal to?

• The average of the lengths of the legs

• The difference of the lengths of the legs

• The square of the length of the hypotenuse

• The product of the lengths of the legs