Perpendicular Bisectors & Midpoint Practice
If there are three non-collinear points on a coordinate plane, name two 2D shapes that can be formed.
What is a triangle and a circle?
What is the solution to a system of two equations? 50 bonus points for the correct formatting.
The intersection of the two equations, written as a coordinate pair (ex. (x, y)).
How can you approximate an inverse of a matrix using your calculator?
ex. [A]-1
When is using the determinant not necessary?
What is when the matrix is collinear with the unit circle or when the determinant is 1?
What are the non-oblique common-sense boundaries for a real world solution set in the coordinate plane?
What is y≥0 and x≥0?
What is the midpoint of the line segment beginning with (4, 8) if it is collinear with a point that is located at the origin?
What is (2, 4)?
Find the exact solution of the following system:
{4x + 9y = 3
{2x + 11y = 20
(Pretend the two brackets are one long one that extends to fit both equations.)
(-146/26, 37/13)
Solve for X: (T(4, -7) o X) = T(6,2)
What is X = T(2, 9)?
Give the inverse of a matrix for an origin centered rotation with a magnitude of 64 degrees.
[cos(-64) -sin(-64)]
[sin(-64) cos(-64)]
What does the Kite Theorem state?
Any point on the perpendicular bisector of a line segment is the same distance from each end of that segment (I'll also take divides the segment in half + both sides are equal).
A triangle has points at (0, 8), (12, 0), and the origin. What is the perpendicular bisector line that goes through the midpoint of (0, 8)?
What is y - 4 = 0(x - 0)
or y = 4?
What kind of x and y intercepts will not be collinear with the real-world accepted answers (hint: materials) to a system of equations for a factory?
X and y intercepts with a negative number for the first or second coordinate.
What does "calculator friendly" mean (Hint: for 2x + 4y = 6, format)?
An equation with y isolated.
What is the inverse of [89 93]?
[34 62]
[62/2356 -93/2356]
[-34/2356 89/2356]
If there is the system {5x + 2y ≤ 33, then is (3, 14)
{4x + 2y ≤ 11 feasible?
What is unfeasible?
If a triangle has its vertices located at (5, 14), (12, 14), and the origin, give the circumcenter's coordinates.
What is (17/2, 34/7)?
A cupcake factory uses two different kinds of flavors for their batters: red velvet and vanilla. One batch of cupcakes made from red velvet flavored batter mixes is made by 4 cups of flour and 2 cups of sugar, while one dozen of vanilla flavored batter mixes requires 4 cups of flour and 4 cups of sugar. The factory only has 18 cups of flour on hand and 10 cups of sugar on hand every day. What would be the best solution of making red velvet and vanilla batters for the cupcakes to satisfy the intersection of the system?
What is (4, 1/2)?
(4 red velvet mixes and 1/2 of a vanilla mix).
Solve for X: [20 19] . [x] = [15]
[9 4] [y] [23]
What is X = [29/7]?
[-25/7]
Represent the system {2x + 5y = 6 as a matrix
{-3x -4y = 14 equation.
What is [2 5] . [x] = [6]?
[-3 -4] [y] [14]
What mode is your calculator regularly on?
Function Mode
Give the center(not rounded, exact) and radius of the circumcircle rounded to three decimal places of a triangle with its vertices located at (3, 3), (4, 7), and the origin.
What is (23/22, 277/77) and 3.746?
For the cupcake problem: A cupcake factory uses two different kinds of flavors for their batters: red velvet and vanilla. One batch of cupcakes made from red velvet flavored batter mixes is made by 4 cups of flour and 2 cups of sugar, while one dozen of vanilla flavored batter mixes requires 4 cups of flour and 4 cups of sugar. The factory only has 18 cups of flour on hand and 10 cups of sugar on hand every day.
Give a number of real-world solutions for red velvet mixes and vanilla mixes to be made every day that make maximum use of the supplies of flour and sugar available for either red velvet mixes or for vanilla or for both.
(0, 2.5) (5, 0) (4, 0.5)
Solve for X: R-35 o X = R245.
What is X = R280?
Find the solution of the system created from two lines that cross through the origin, one passing through (8, 2) and one passing through (4, -2).
What is (0,0)?
A line passes through points (8, 3) and (10, 1). Give the equation of the line in ax + by = e form and their x and y intercept coordinates.
What is x + y = 11 and (0, 11) and (11, 0)?