Find the perimeter of the triangle whose vertices are the following specified points in the plane. (- 10, – 4), (9, –3) and (-2, – 10)

Q: Find the area of the triangle whose vertices are A(-6, 0), B(10, -5), C(-2, 4)

A: We know that the area of a triangle ABC with vertices Ax1,y1, Bx2,y2, Cx3,y3 is:…

Q: Find the area of the triangle whose vertices are A(-1, -1), B(3, 3), C(2, 1)

A: Given: Find the area of the triangle whose vertices are A(-1, -1), B(3, 3), C(2, 1)

Q: Find equations for the line perpendicular to the triangle (PCQR) and through the point (P) if…

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Q: Find the coordinates of a fourth point so that the four points form the vertices of a rectangle. 64…

A: We have to find the coordinates of the fourth vertex to make it a rectangle.

Q: Find equations for the altitudes of the triangle with vertices A(-3, 2), B(5, 4), and C(3, -8), and…

A: Given,           Altitudes of the triangle with vertices A(-3,2), B(5,4) and C(3,-8)

Q: Find the coordinates of the vertices A, B, and C of the rectangular box shown to the right. (0,0,8)…

A: Given,  A rectangular box with coordinate of two vertices are 4, -7, 0  and  0, 0, 8    We have to…

Q: Find an equation of the set of all points equidistant from the points A(-1, 5, 4) and B(6, 2, –1).

A: Given : A(-1,5,4) and B(6,2,-1) Let P(x,y,x) be at equidistance from A  and B Now find the distance…

Q: Find the distance between each pair of points: a) (-3, - 7) and (2, 5) b) (0, 0) and (- 2, 6) c)…

A: We have to find the distance between each pair of points: a) -3, -7 and 2, 5 b) 0, 0 and -2, 6 c)…

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: Find the points on the coordinate plane 2,3) and Q(2.-2.-1)

A: Given query is to find point P and Q on coordinate plane.

Q: The distance from (-3,-4,-7) to the xz-plane is (A) -4 (B) (C) -3 (D) 3 (E) 4.

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Q: The coordinates of the vertices of a rectangle WIND are W(-2, 6), I(10, 6), N(10, -3), and D(-2,…

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Q: In the triangle with vertices (2, 0), (3, 2), (4, - 3), find the equations of the altitudes, and…

A: Let ABC be the △ with vertices A3,2 , B2,0 , C4,-3 and AD altitude of △ABC drawn from vertex A. Let…

Q: Suppose A(-9, -8) and B(-4, -6). What is the x coordinate of the midpoint for AB?

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Q: find all points on the y-axis that are a distance of 6 from the point (3,-1)

A: Let the point is (0,y).

Q: Find all points on the y-axis that are a distance 13 from P(12, 6).

A: To find: All the points on y-axis that are a distance 13 from P12,6. Concept used: The x-coordinates…

Q: The distance from (-3,-4,-7) to the yz-plane is (A) -4 (B) 4 (C) -3 (D) 3 (E) 7

A: The distance(d) between two points (x1,y1,z1) and (x2,y2,z2) in a cartesian coordinate system is…

Q: Write the coordinates of the vertices after a reflection over the line y = 1. 104 8. -10 -4 -2 2 4.…

A: The reflection of the given image would be as shown in the below diagram.

Q: Find the perimeter of the triangle whose vertices are the following specified points in the plane.…

A: The vertices of the triangle are (-9,-5), (-6,1), (5,8)

Q: The distance from (-2,-5,-6) to the yz-plane is (A) -2 (B) 2 (C) (D) -5 (E) 6

A: Use distance between two points

Q: Find the area of the triangle that lies in the first quadrant (with its base on the x-axis) and that…

A: y=2x-4 and y=-4x+20 We need to find the area of the triangle that lies in the first quadrant (with…

Q: Write the coordinates of the vertices after a reflection over the line y = 2. 104 6. F E -10 -8 -6…

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Q: Find the point on the x-axis that is equidistant from the points (0,−1) and (5,−3)

A: To find the coordinates of the point satisfying the given conditions

Q: Write the coordinates of the vertices after a reflection across the line y = x. 101 -10 F 10 D -10…

A: topic - reflection

Q: Find the equation of the perpendicular bisector of th segment joining the points A(2, 3) and…

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Q: 10. Quadrilateral ABCD with vertices A(-4, -1) B(0, -2), C(-1, -6), and (-6, -3) in the y-axis. A'(…

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Q: How would i determine whether the three points are collinear?   (0,-7), (-3,-21), (2,3)

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Q: Determine whether the four vertices form a parallelogram: P(1, - 4), Q(3, 11) , R(6, 11), S(4, - 4)…

A: Diagonals of parallelogram bisect each other.So we will find  mid points of each diagonal and see if…

Q: Find the area of the triangle formed by the lines 5x + y – 14 = 0, x+ 7y + 38 = 0, and 9x – 5y + 2 =…

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Q: Find the area of the rectangle ABCD with vertices 4(-3,0), B(3,2), (4,-1), and D(-2,-3) B(3,2) 2…

A: Area of rectangle is length× Breadth

Q: Find the area of the parallelogram with the vertices A(-1,2,4), B(0,4,8), C(1,1,6), and D(2,3,10).

A:

Q: The midpoint of AB is at (-3,-2) if A= (10,-1) find B

A: Answer is - B = (-16,-3).

Q: Find the areas of the triangles whose vertices are given A(-6, 0), B(10, -5), C(-2, 4)

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Q: Find the area of the parallelogram whose vertices are: A(0,0,0) B(5,2,6) C(9,-1,6) D(4,-3,0)

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Q: Find the area of the parallelogram with vertices: P(0,0,0), Q(-4,-5,4), R(-4,-3,6), S(-8,-8,10). 0

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Q: Find the center of the circle x² + y² - 8x = 2. Select one: O a. (4,0) O b. (0,4) O c. (0-4) O d.…

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Q: Find the area of the parallelogram with vertices A(-3, 0), B(-1, 6), C(8, 5), and D(6, -1).

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Q: Find the distance between the given points. (- 3, 1) and (9, 6)

A: We have to find the distance between two points which we can find using distance formula which is…

Q: Find b so that the points (4,-6), (5,-8), and (b,-2) lie on the line

A: Please find the solution in the attached images :

Q: The coordinates of the vertices of a triangle are M (-4,1), A (3,3) and B (2,-3).

A:

Q: Find the distance from the point P(-1,3,-5) to the plane through the three points Q(3, 1, -3). R(4,…

A: The points passing through the plane are: Q3, 1, -3R4, 6, -5S5, -4, -6

Q: Find the area of a triangle with the points A (-16, 8,-8B(-15, -1,0C (-1,-2,-12s it vertices by…

A: The area of the triangle with vertices A, B, C is given by: Area =12(A-C)×(B-C)...(1) The given…

Q: Find all points on the y-axis that are 5 units from the point (4, 4).

A: Distance between two points (x1,y1) and (x2,y2) on the graph is given by the distance formula, that…

Q: Determine whether the four vertices form a parallelogram: D(2, - 4) , E(4, 8), F(10, 8), G(8, - 4) .

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Q: A rectangle has a vertex at J(2, 2), H(4, −2), and G(−2, −5). What are the coordinates of the fourth…

A: You know that the diagonals of a rectangle bisect each other.

Q: Are the points A(2, – 3), B(5, 1), and C(-4, - 11) collinear?

A: Given:A2,-3 , B5,1 and C-4,-11 collinearAB=AC+BCd=x2-x12 + y2-y12

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.