Reflect TAB over the line y=2, and then translate by the rule (x,y) -> (x-5,y-4). Fill out the table and graph all images. ТАВ T'A'B' T"A"B" T (2,3) A (1,1) в (4,-3) 6-54 -3 -2-10 -2

Q: intercept = 3

A: Given query is to find the equation of the line.

Q: Find the number a that makes the point (6, a) line on the line that contains the points (−2, −1) and…

A: L

Q: Write the point-slope form and the slope-intercept form of the line passing through (1, 3) and (3,…

A:

Q: Graph a horizontal line going through the point (5, 2).

A:

Q: (5, 0) (-2,-5)

A:

Q: Which set of coordinates follows these two rules? • X-coordinate: Start with 4 and add 4 to each…

A:

Q: what about the x and y intercepts

A: X-intercepts are given by substituting f(x)=0 and y-intercept is given by substituting x=0 in f(x).

Q: A line passes through the points (-3, 4), (7, -2), and (17, y). What is the value of y?

A:

Q: Find the midpoint of the line segment with endpoints (1, 2) and (7, -3).

A: Given  The line segment with endpoints (1, 2) and (7, -3).   Midpoint formula :- x, y=x1+x22,y1+y22

Q: Write an equation in slope- intercept form for the line through a) (-4, 8) and (2, -3) b) (5, 3) and…

A:

Q: Graph the line 3y = 3 X 4

A:

Q: Find the slope-intercept form for the line parallel to - 5x +7y = 35 and passing through the point (…

A:

Q: Parameterize the line segment that starts at (3,2) and ends at (-10,5).

A: I am attaching image so that you understand each and every step.

Family of Curves

A family of curves is a group of curves that are each described by a parametrization in which one or more variables are parameters. In general, the parameters have more complexity on the assembly of the curve than an ordinary linear transformation. These families appear commonly in the solution of differential equations. When a constant of integration is added, it is normally modified algebraically until it no longer replicates a plain linear transformation. The order of a differential equation depends on how many uncertain variables appear in the corresponding curve. The order of the differential equation acquired is two if two unknown variables exist in an equation belonging to this family.

XZ Plane

In order to understand XZ plane, it's helpful to understand two-dimensional and three-dimensional spaces. To plot a point on a plane, two numbers are needed, and these two numbers in the plane can be represented as an ordered pair (a,b) where a and b are real numbers and a is the horizontal coordinate and b is the vertical coordinate. This type of plane is called two-dimensional and it contains two perpendicular axes, the horizontal axis, and the vertical axis.  

Euclidean Geometry

Geometry is the branch of mathematics that deals with flat surfaces like lines, angles, points, two-dimensional figures, etc. In Euclidean geometry, one studies the geometrical shapes that rely on different theorems and axioms. This (pure mathematics) geometry was introduced by the Greek mathematician Euclid, and that is why it is called Euclidean geometry. Euclid explained this in his book named 'elements'. Euclid's method in Euclidean geometry involves handling a small group of innately captivate axioms and incorporating many of these other propositions. The elements written by Euclid are the fundamentals for the study of geometry from a modern mathematical perspective. Elements comprise Euclidean theories, postulates, axioms, construction, and mathematical proofs of propositions.

Lines and Angles

In a two-dimensional plane, a line is simply a figure that joins two points. Usually, lines are used for presenting objects that are straight in shape and have minimal depth or width.