Midpoints & Distance
The formula to find the point halfway between two given points.
(What is the midpoint formula?.
This describes the slope of horizontal lines.
(What is 0?)
This is the slope-intercept form of a line.
(What is y = mx + b?)
This formula helps prove two segments are congruent.
(What is the distance formula?)
This is the general equation of a circle centered at (h, k).
(What is (x - h)² + (y - k)² = r²?)
The midpoint between (2, 4) and (6, 10).
What is (4, 7)?
This type of line has an undefined slope.
(What is a vertical line?)
A line passes through (0, 5) and has a slope of -2. This is its equation.
(What is y = -2x + 5?)
To prove a quadrilateral is a rectangle, show these relationships.
(What are opposite sides congruent and adjacent sides perpendicular?)
The radius of the circle with equation (x - 3)² + (y + 2)² = 49.
(What is 7?
This formula is used to find the length of a segment on the coordinate plane.
(What is the distance formula?)
Lines with the same slope are this type of line.
(What are parallel lines?)
A line with slope 4 and y-intercept -1.
(What is y = 4x - 1?)
To prove a triangle is isosceles, you can do this.
(What is show two sides are the same length using distance formula?)
The center of the circle given by x² + y² = 81.
(What is (0, 0)?)
A student finds the midpoint of a segment as (3, 2), but the endpoints were (2, 4) and (4, 0). Identify the mistake.
(What is not averaging x- and y-values correctly?)
The slope of a line perpendicular to a line with slope 2.
(What is -1/2?)
Write the equation of a line perpendicular to y = 3x + 2 and passing through (3, 1).
(What is y = -1/3x + b, then solve using the point?)
A quadrilateral has two pairs of parallel sides. This proves it's this shape.
(What is a parallelogram?)
Write the equation of a circle with center (5, -2) and radius 6.
(What is (x - 5)² + (y + 2)² = 36?)
Use the distance formula to determine whether the triangle with vertices (0,0), (0,4), and (3,0) is a right triangle.
(What is yes, by confirming the Pythagorean Theorem?)
A student says two lines are perpendicular because their slopes are negative. Why might this be wrong?
(What is they must be negative reciprocals, not just both negative?)
What is the difference between standard form and slope-intercept form of a line?
(What is Ax + By = C vs. y = mx + b?)
A student wants to prove a quadrilateral is a square using coordinate methods. These steps will prove it.
(What is show four congruent sides and four right angles using distance and slope?)
A student says the radius of the circle (x + 1)² + (y - 4)² = 30 is 30. Explain the mistake.
(What is the radius is √30, not 30?)