The coordinates of the vertices of a rectangle are given by R(- 3, – 4), E(– 3, 4), C (4, 4), and T (4, – 4). Plot these points on the coordinate plane at the right and connect them to draw the rectangle. Then connect points E and T to form diagonal ET. 5 a. Use the Pythagorean Theorem to find the exact length of ET. b. How can you use the Distance Formula to find the length of ET ? Show that the Distance Formula gives the same answer.

Q: QR is located at Q(-5, -8) and R(-1, 3). Which pair of points would form a segment congruent to QR ?…

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Q: A В C 3X +4 5X - 6

A: B is the midpoint of AC⇒ AB=BC

Q: In the diagram below ABC has verticles at A (-7,8) B (7,0) and C (-5,-8) Show that point A is…

A: Given ABC has vertices atA(-7,8)B(7,0)C(-5,-8)Distance between twovertices (x1,y1) &…

Q: Given the points A(4, 6), B(r, 7), C(6, s). If B is the midpoint of AC, find the value of rand the…

A: Given: The points are A-4, 6, Br, 7 and C6, s. The midpoint of two points a, b and c, d is a+c2,…

Q: 90, tind, to the nearest tenth, ed uf the circle containing AB. y-axis А (3, 7) B (11, 5) X-axis

A: Result used: Area of circle =πr2

Q: C. Answer each of the following : 1. Which of the following points is nearest to ( 3,4) ? а. (4,0)…

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Q: If GK =t+ 21 and IK = 3t - 21, find the value of t in parallelogram GHIJ. %3D I H. K t =

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Q: The points P: (-2,0,0), Q: (0,1,1) and R: (1,2,1) are givena. determine the angle in the triangle…

A: Solution  a) To determine the angle at corner Q in triangle ΔPQR, we can use the dot product…

Q: in standard position, and the unit circle. The value of b can be written in t are whole numbers. ues…

A: we will find the required.

Q: Consider points A(4, -1, 3), B(3, 1, 8), and C(1, -3, -3). (a) Find the area of parallelogram ABCD…

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Q: A circle is centered at the point (– 2, 5) and has a radius of 6 units. a. Which points on the…

A:

Q: 8 units away from

A: Given that: Coordinates of A(0,0) and B(12,5)C is 8 units away from AB.

Q: Let A(1,3), B(3,1) and C(0, -2) be the vertices of a triangle ABC. Plot the vertices B, C, compute…

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Q: The diagonals of parallelogram JKLM intersect at P. If PM = 3x – 2, PK = x + 3 and PJ = 4x – 3, find…

A: Use parallelogram properties

Q: 1. Consider triangle AABC on the coordinate plane. Let P = (-2, 1) and Q = (2,1). Point P is on side…

A: We are authorized to solve only 3 subpart of question, please repost remaining parts

Q: In the diagram, A is located at (0, 0), G is located at (5, 4), and I is located at (8, 4). Find the…

A: Given points: A is (0,0) G is (5,4) I is (8,4) Let the length of AC be 2a. Therefore, AF = CF = a…

Q: In the problem we use the distance formula. Show that the triangle with vertices A(0,2), B(-3,-1),…

A: We have to show that the triangle with vertices A(0,2), B(-3,-1), and C(-4,3) is isosceles.

Q: In the figure, P(-4,3), Q(-2,-4), R(k,-17/2) and S(1,2) are four points on a rectangular coordinate…

A: The given points are:P=(-4, 3)Q=(-2, -4)R=k, -172S=(1, 2)

Q: Find the lengths of the sides of the triangle given by the points P(2, –1,0) and Q(4,1,1) and R(4,…

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Q: Exercise 1.12. Determine the cosine of the angles of the triangle whose vertices are A = (2,-1, 1),…

A: We can find the length of all the three sides then with the help of cosine rule of triangle we will…

Q: Given points S = (2,4,-2), T= (-2,-2,1) and V= (5,1, -1), determine the coordinates of the point D…

A: The objective of this question is to find the coordinates of the point D on line ST that is closest…

Q: Find the length and direction of (1, –4, –5). Length is Direction is

A: See attached file for a step by step explanation to find the length and the direction of vector.

Q: intersect each other at

A: It is definition of the Origin

Coordinate Geometry

Coordinate geometry, also known as analytic geometry or Cartesian geometry in classical mathematics, is a type of geometry that is studied using a coordinate system. Coordinate geometry is a branch of mathematics that describes the position of points on a plane using an ordered pair of numbers called coordinates.