Exploring Distance and Midpoint Formulas

What is the definition of a midpoint in geometry?

• A point that is always at the origin

• A point that is always at the end of a segment

• A point that divides a segment into two congruent parts

• A point that divides a segment into two unequal parts

What does the term 'congruent' mean in the context of geometry?

• Having the same size but different shapes

• Being parallel to each other

• Having the same shape but different sizes

• Having the same size and shape

Which of the following can be a bisector?

• A point

• A line

• A plane

• All of the above

If a segment RS is bisected by point T, and RT is 21.7 units, what is the total length of RS?

• None of the above

• 21.7 units

• 43.4 units

• 10.85 units

In an algebraic problem, if point C is the midpoint of BD, and BC is represented by 3x - 2, what is the value of x if BD is represented by 2x + 3?

• 5

• 2

• 1

• 3

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

• ((x1 + x2) / 2, (y1 + y2) / 2)

• ((x1 / x2) / 2, (y1 / y2) / 2)

• ((x1 - x2) / 2, (y1 - y2) / 2)

• ((x1 * x2) / 2, (y1 * y2) / 2)

Which of the following is the correct distance formula between two points (x1, y1) and (x2, y2)?

• sqrt((x2 / x1)^2 + (y2 / y1)^2)

• sqrt((x2 + x1)^2 + (y2 + y1)^2)

• sqrt((x2 * x1)^2 + (y2 * y1)^2)

• sqrt((x2 - x1)^2 + (y2 - y1)^2)

If the midpoint of segment AC is M(3, 4) and A is at (1, 6), what are the coordinates of point C?

• (5, 2)

• (3, 4)

• (1, 6)

• (7, 8)

Given points P(-2, 5) and R(4, 3), what is the distance between P and R?

• 8 units

• 7.21 units

• 5 units

• 6.32 units

If the distance between points A(2, 3) and B(5, 7) is calculated using the distance formula, what is the result?

• 4 units

• 5 units

• 3 units

• 6 units