Translation T maps the point (1, 3) to (2, 6). Which of the following rules describes the translation T? OT:(z,9)→ (2z, 2y) OT:(-,4) (-,) OT:(2,4) (z-1,y-3) OT:(2,9)→ (z +1,y+3)

Q: What is the coordinates of P₁ if (1,-2,8) is the midpoint between P₁(x1,1,Z1) and P2(-4,5,6)?…

A:

Q: What is the translation image of (-2, -7) after the translation of (x, y) → (x + 2, y + 3)?

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Q: Which of the points P(1, -2) or Q(8, 9) is closer to the point A(5, 3)?

A: The two two points on cartesian scale is P(1,-2) and Q(8,9) The fixed point from distance is to…

Q: What is the reflection over the y-axis of (-7,8)

A: Given  Point : (-7,8)

Q: * Find the Cartesion Coordinates of the points. (),(万,). (-2,2)

A: To convert Polar coordinates r, θ to Cartesian coordinates x, y apply:x=rcosθ   y=rsinθ

Q: , x); R = [0, -) D) D = (-, x); R = [-10, -)

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Q: What are the coordinates of the point on the directed line segment from (-6, –6) to (-4, 10) that…

A: we have to find point

Q: Show that the line [3, 2, 3] passes through the point of intersection of the lines [2, 1, 1] and…

A: It has to be proved that the line 3,2,3 passes through the point of intersection of the lines 2,1,1…

Q: If a translation maps point (3, 2) to (4, 5); or T: (3, 2)  (4, 5), then what is the image of the…

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Q: Find the midpoint of AB if A(-3, 8) and B(-7,-6). O (-5, 1) O (1,-5) O (1,5) O (-5, 2) Previous Next

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Q: Determine the new order pairs if the points are reflected across the y- axis. J(2, 2), K(7, 4), L(9,…

A: Given- J2,2,K7,4,L9,-2 and M3,-1 To determine-  The new order pairs if the points are the reflected…

Q: Determine the new coordinates of the point (3,5) when the origin is moved to (2,4) by translation…

A: We have to find the point

Q: Which one of the points P(6, 9, -3), Q(8, -2, -8), R(-5, 8, 1) in 3-space is closest to the…

A: We have to find closest point to the xz plane from given points P, Q and R. Topic:- 3D vector.

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.