considerer the following three points A=(-1,-1), B=(1,3) and c=(3,7) a) find the three distances AB, BC and AC b) use the results of (a) to show that the points are collinear (a line straight of line)

Q: C(3,-5) and D(7,9)

A: Topic:- coordinate geometry

Q: The coordinates of P are (2,0) and the coordinates of Q are (0,-6). Find the midpoint of segment PQ.

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Q: e coordinates of the fourth point D such that the p D as parallel, and the lines AC and BD as…

A: Three given points are: A=4,4 ; B=6.84,1.16 ; C=6.84,6.84 We have to find the coordinates of the…

Q: Find the distance from (-5, 9, –12) to each of the following: 1. The xy-plane. Answer: 2. The…

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Q: 8. On parallelogram ABCD below, if A(1, 1), B(8, 5), C(5, -5) and D(-2, -9), what are the…

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Q: Parallelogram ABCD has diagonals AC and BD that intersect at point E as shown. Which of the…

A: Given that:

Q: 3. a) If ā = (2,3,7) and b = (-4, y,-14), for what values of y are äand b perpendicular? For what…

A: Note to student : Hello. Thanks for posting your queries. Let us inform you that your question has 2…

Q: Find all points with coordinates of the form (a, a) that are a distance 3 from P(-2, 1).

A: Given: P(-2,1) and distance is 3. To find the other coordinate point.

Q: Use a projection to derive a formula for the distance from a point (x,y) to the line ax+by=c, where…

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Q: Plane P contains four distinct lines L,,l,, and l. Suppose 1,lG.21,and l, II . How are l, and 4…

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Q: plane so that A is (0, 0), B is (a, 0), Cis (a, b), and Dis (0, b). What formula can he use to…

A: We can answer the given question as below.

Q: A,B,C are three points on OX ,OY ,OZ respectively at distance a,b,c (a'0,b'0,c'0)from the origin…

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Q: V and S are the midpoints of the legs, QU and RT, of trapezoid QRTU. If TU = 6 and QR = 10, what is…

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Q: Q2 |The points A(1,0), B(2,0), C(4,2), and C(xy) are the verticies of a parallelogram. Find x and y,…

A: We will find the fourth vertex (x,y) of the parallelogram .olso we will find perimeter and area of…

Q: Use the diagram to determine whether the statement is true or false. 1. Points D, G, and F are…

A: given diagram is                                                       Lines m and k are parallel…

Q: 28. Given the points A(3, 2) and B(7, -6) what is the point halfway between A and the midpoint of…

A: To solve the following problem

Q: 4.(a, b), (c, 0) 5.(2a+c, 2d), (2b-c, 2c)

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Q: 4) The point M is the midpoint of AB , where AM = 3x +8 and MB = 6x- 4, find AB

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Q: Q3. Find the distance between the points AB and BC where A is (2,1,0), B is (-1,3,1) and C is (-1,…

A: The points A2,1,0, B-1,3,1 and C-1,0,1 we have to find the distance between the points AB and BC…

Q: Let T1 and T2 be two triangles in the plane. Find the number of possible points of intersection of…

A: Given, T1 and T2 are two triangles in a plane  To find the number of possible points of intersection…

Q: parallelogram. I L and M are the midpoint o E amd tespetively express AL and AM in terms of that AI…

A: Given: ABCD is a parallelogram. L and M are the midpoints of BC→ and CD→ respectively. It is to…

Q: 2. If B is the midpoint of AC, which of the following must be true? I. AB + BC = AC II. 2RC = AC 1.…

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Q: a) Plot the given points on the Cartesian plane and also find and plot the midpoint. A(H,-T), B (Τ,…

A: H=0,  T=7  &  U=0 a). AH, -T=A0, -7BT, U=B7, 0 Now the mid point is, 0+72, -7+02=3.5, -3.5…

Q: 1. Which statement correctly represents the distance between points E and F? (0,0,5) A 0.0.0 ++++ B…

A: NOTE: Refresh your page if you can't see any equations. . the  coordinate of E and F are

Q: determine the points that are symmetric with respect to (a) the x axis, (b) the y axis, and (c) the…

A: Given that the point (5, 0) a) symmetric with respect to the x axis Substitute the coordinate -y for…

Q: determine the points that are symmetric with respect to (a) the x axis, (b) the y axis, and (c) the…

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Q: What will be the new coordinates of the triangle with vertices A(0,1),B(1,2) and C(1,0) when : i) it…

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Q: 1. On a coordinate plane, DEF has vertices D(1, 2), E(7, 2) and F(1, 9). What is the distance…

A: Since, distance bewteen two points is given by:-d=x2-x12+y2-y12

Q: On line segment PQ, R is the midpoint of PQ and midpoint of RQ so that are P(-13,25) and Q(23,43).…

A: using mid point formula if P= (a,b) and  Q= (c,d) is the line segment and R= (x,y) is  the mid point…

Q: In parallelogram WXYZ, diagonals WY and XZ intersect at point A. Give WA = x^2 - 48 and AY = x^2 -…

A: We have to find WY

Q: (c) Find the distance from the point (4, 22, 6) over to the xz-plane. (d) Find the distance from the…

A: c) To find the distance from point (4, 22, 6) to xz-plane. Here  x = 4, y = 22, z = 6.     Let us…

Q: The distance between the points (-3,-5) and (2, 7) on the coordinate plane is given as V3 +t, What…

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Q: ind the distance from the point to the plane ( 2,–3,4) x + 2 y – 2 z = 13

A: To find : Distance from the point (2,-3,4) to the plane x+2y-2z=13   formula for distance from point…

Q: 3. Find the distance between points P₁ and P2. (a) P₁(-1,1,5), P₂ (2, 5,0) (b) P₁(3,4,5), P₂(2, 3,…

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Q: The coordinates of the points O, A and B of the plane are (0.0), (0.20) and (300.0), respectively. A…

A:

Q: The midpoint of AB is M (0, –4). If the coordinates of A are (-8, –7), what are the coordinates of…

A: To find the coordinate of point B. If the coordinate of point A and midpoint of line AB is given.

Q: 29.) Find the distance from the point (-3,4,3) to the origin. (а) 3 (b) 5 (c) 3/2 (d) 34 (e) None of…

A: Find the distance from the point (-3,4,3) to the origin

Q: In Exercises 7 and 8, the endpoints of JK are given. Find the coordinates of the midpoint M. J(-3,…

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Q: ABC is a triangle. BF, CG are any two lines drawn from the extremities of the base BC to meet AC and…

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Q: Find the point with coordinates of the form (3a, a) that is in the third quadrant and is a distance…

A: Given data: The distance between points is s = 5. Given point is P(1, 2).

Q: Q1: Determine the coordinates of point N (zero, ?, ?) located on the line AB where: A(-4,5,6) B…

A:

Q: Give the Cartesian equation of the locus of points P(x, y) given that P is 5 units from the point…

A: Any point on the Cartesian plane is represented as x, y. The locus is a set of points on the…

Q: 12. Find the distance between the parallel lines x = -4 -t 4:{y = -3+ 2t, teR and l2: y = -5 – 2s, s…

A: Given,  l1=x=-4-ty=-3+2tz=3-2t, t∈ℝ &l2=x=6+sy=-5-2sz=5+2s, s∈ℝ represented as,  l1=-4, -3,…

Q: Exercises 1 and 2 refer to points X(- 2, – 4), Y(2, 4), and Z(2, - 6). 1. Graph X, Y, and Z on one…

A: since you have posted multiple questions so we solve the first question for you,to get the remaining…

Q: (a) If we mark off a distance t along the unit circle, starting at (1, 0) and moving in a…

A: Topic -  unit circle

Q: Let's consider points X and Y on the coordinate plane below. y Y (x2, Y2) x (x1,Y1) Write a formula…

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Q: following represents the nidpoint formula? A. M= (, ) B. M = (, ) C. d = (x2 – x1)² + (ý2 – y1)² D.…

A:

Q: In this exercise we use the Distance Formula and the Midpoint Formula. If M(1, 7) is the midpoint of…

A: mid point formula  x =(x1 +x2)/2 y =(y1 +y2)/2

Q: (ii) Find the point of intersection of the lines L : r = (1,2) + t(2, – 1), –0o < 1 < +oo and L2 : r…

A: Here we find the intersecting point.

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.