Given a square, describe how to use a compass and a straightedge to construct a square whose area is a. twice the area of the given square. b. half the area of the given square. a. Choose the correct answer below. O A. Draw perfect 90" angles, then make the sides of the square four times the length of the original square. This would result in an area that is twice the original area. O B. Let the length of the side of the square be s. Draw the side of the square and make the new square have diagonal lengths equal to the side. Then the area is (V2 s) = 25. O C. Let the length of the side of the square be s. Draw the diagonal of the square and make the new square have side lengths equal to the diagonal. Then the area is (v2s)=25. O D. Draw perfect 90° angles, then make the sides of the square twice the length of the original square. This would result in an area that is twice the original area. b. Choose the correct answer below. OA. V2s Make the lengths of the sides of the new square 5 the length of the diagonal, or W2s then the area of the new square is (号 O B. Draw perfect 90° angles, then make the sides of the square a quarter the length of the original square. This would result in an area that is half the original area. Oc. (今) Make the lengths of the diagonals of the new square = the length of the side, or (号 then the area of the new square is O D. Draw perfect 90° angles, then make the sides of the square half the length of the original square. This would result in an area that is half the original area.
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.
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