Coordinate Proof Using Distance and Midpoint

10.4 Coordinate Proofs Using Dist. Form. & Midpoint Formula (We Do)

" The only way to learn mathematics is to do mathematics." -Paul Halmos

Multiple Choice

What point is halfway between (3, -1) and (8, -6)?

• (11, -7)

• (-5.5, -3.5)

• (5.5, -3.5)

• (2, -2)

Multiple Choice

What is the center of MN given M(3, -1) and N(7, -5)?

• (5, -2)

• (10, -6)

• (5, -3)

• (2, -2)

Multiple Choice

Which of the following is the correct midpoint formula given two endpoints (x₁, y₁) and (x₂, y₂)?

Multiple Choice

Given two points (x₁, y₁), (x₂, y₂) the distance between them is:

Multiple Choice

Find the distance between the two points.

$$d=\sqrt{\left(x_2-x_1\right)^2+\left(y_2-y_1\right)^2}$$  

• 7.1

• 7.8

• 8.7

• 8.9

Multiple Select

• Find the midpoint of the diagonals.

• Find the length of the diagonals.

• Find the slope of the diagonals.

• Diagonals in a rhombus are not perpendicular, so this is not a good method.

Multiple Choice

1

• Find the lengths of the diagonals.

• Find the slope of each diagonal.

• Find the midpoint of each diagonal.

• Find the midpoint of each side.

Multiple Choice

• AB = CD

• AB = CD and BC = AD

• mCD ∙ mBC = -1

• mAB = mCD

Multiple Choice

What is the midpoint between (3, -1) and (7, -5).

• (5, -2)

• (10, -6)

• (5, -3)

• (2, -2)

Multiple Choice

Which formula is used to determine if two lengths are bisecting?

• Slope

• Midpoint

• Distance

Multiple Choice

How many times should we use the distance formula to determine if a quadrilateral is a parallelogram?

• 1

• 2

• 3

• 4

Multiple Choice

Analyze the graph. Using distance formula, can you prove this parallelogram is a rectangle?

• Yes, because AD = BC = 10 and AB = CD = 5

• No because  $$AD=2\sqrt{10}$$  and  $$BC=10$$   

• Yes because AD = BC = 5 and AB = CD = 10

• No because  $$CD=\sqrt{73}$$  and  $$BC=5$$