For Exercises 19–22, determine if the given points form the vertices of a right triangle. (See Example 2) 19. (1, 3), (3, 1), and (0, –2) 20. (1, 2), (3, 0), and (-3, –2) 21. (-2, 4), (5, 0), and (-5, 1) 22. (-6, 2), (3, 1), and (1, –2)

Q: Do the points (1, 0,−1), (0, 2, 3), (−2, 1, 1), and (4, 2, 3) lie in the same plane? Justify your…

A: To check: If the points (1, 0,−1), (0, 2, 3), (−2, 1, 1), and (4, 2, 3) lie in the same plane and…

Q: What is the image of (-8,10) when reflected in the y-axis? OA. (8, -10) Ов. (10, 8) OC. (-8, -10)…

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Q: What are the coordinates of P(−4, −8) after it has been reflected about the x-axis? (x, y) =

A: The given point is,

Q: Find the coordinates of the point plotted below 6+ 4 -6 -5 -4 -3 -2 -1 i 2 3 4 5 ở -2 -3 -4 -5 9- If…

A: NOTE: Refresh your page if you can't see any equations. . when the point  is reflected across the…

Q: What are the coordinates of (-4, 1) after a reflection over the y-axis? 10- 8- 6+ 4+ (-6, 1) (-4, 1)…

A: Given, The coordinates of point -4, 1  We have to find the coordinates of point -4, 1 after a…

Q: Find the distance between the pairs of points in exercises A) (0,0,0) and (2,-1,-2) B)…

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Q: If a triangle has vertices (-5,-5), (-4,-6), and (-2,-1), how do you reflect this over the y=x axis

A: First of all to find the coordinates of the vertices A(-5,-5),B(-4,-6),C(-2,-1) after reflection…

Q: In Exercises 25–30, find the distance between points P1 and P2. 25. P1(1, 1, 1), P2(3, 3, 0) 26.…

A: Given,

Q: A triangle has vertices A (-2,3), B (0,0) and C (1,2) What are the coordinates of the triangle if it…

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Q: 4. Suppose the point B(2,8) is reflected across the x-axis and then translated according to the rule…

A: I am going to solve the given problem by using some simple geometry.

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

A: Given  Point : (-7,8)

Q: Find the point of intersection of the lines: y = 4x + 1 and y = -2x +4 %3D o (2,9) 으(4,2) ㅇ (4,3) O…

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Q: Show that the points A(3,-2,4)B(1,1,1,) and C(-1,4,-2) are collinear

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Q: Direction and Midpoints

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Q: Write the coordinates of the vertices after a reflection over the line x = -1. 104 4 -10 -81 -6 -4…

A: Here the figure is reflecting across x=—1, so y coordinates of every point will remains same only x…

Q: Find nature of the triangle formed by the lines x2-3y2=0 and x=2

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Q: Is there a straight line that passes through the points? P, (2,0,1), P2(3, –2,0), P3(1,2,2)

A: If a line is passing through three points, then the points are said to be collinear. The vector that…

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: In Exercises 23-30, find the distance between the two points. (See Example 4.) 23. A(13, 2) and B(7,…

A: For distance between (a,b) and (p,q)distance, d = (a-p)2+(b-q)223) A(13,2) and B(7,10)      AB= d =…

Q: Find the areas of the triangles whose vertices are given in Exercises 41–47. 41. A(0, 0), B(-2, 3),…

A: Since we only answer up to 1 question, we’ll answer the first question. Please resubmit the question…

Q: What are the coordinates of point P, the image of point (3, –4) after Rywx? А. (3.4) B. (-3,4) С.…

A: The point given is (3, -4)

Q: Trapezoid JKLM is shown on the coordinate plane below: 6. -9 -8 -7 -6 -5 -4 -3 -2 J 2 3 456 K -2 If…

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Q: Find the areas of the parallelograms whose vertices are given in Exercises 35–40. 35. A(1, 0), B(0,…

A: Area of parallelogram ABCD is |AB x AD|

Q: Use analytic geometry to classify the quadrilateral with vertices J(-2,1), K(2, 3), L(4, -1), and…

A: We have to classify the quadrilateral

Q: 1)calculate xy dady Where D is a triangle with vertices (0,0), (5,0) and (5,5) tip:Don't use the…

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Q: 9. In the standard (x, y) coordinate plane, line e contains the points (3, 5) and (5,8) and line m…

A: We have to find out k

Q: In Exercises 23-30, find the distance between the two points. (Ser Erample 4. 23. A(13.2) and B(7,…

A: Given that: 23. A(13, 2) and B(7, 10)24.C(-6, 5) and D(-3, 1)25. E(3, 7) and F(6, 5)     NOTE: As…

Q: In Exercises 33–34, find the distance from the point to the line. 33. (3, -1, 4); x = 4 - t, y = 3 +…

A: Note:We’ll answer the 33th question since we answer only one question at a time. Please submit a new…

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

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Q: What are the coordinates of (-4, 1) after a reflection over the y-axis? 10- 8- 6+ (-6, 1)(-4, 1)2+ 4…

A: Given,  The coordinates of point -4, 1  We have to write the coordinates of point -4, 1 after a…

Q: What are the coordinates of the midpoint of segment GH with endpoints G(-2, 5) and H(4, 1)?  a (-6,…

A: midpoint of segment GH with endpoints G(-2, 5) and H(4, 1)

Q: Write the coordinates of the vertices after a reflection over the line x = 3. 10 8 6. 2. -10 -8 -4…

A: Given query is to find the coordinates of the vertices after reflection over x = 3.

Q: What is the image of the point (-5, 2) under the translation T34?

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Q: Show that the point P(3, 1, 2) is equidistant from the points A(2, -1, 3) and B(4, 3, 1).

A: Let the distance between P(3, 1, 2) and A(2, -1, 3) be d1 and the distance between P(3, 1, 2) and…

Q: What is the midpoint of the segment whose end points are (17, 1) and (-9, 3)? A (8, 4) B (4, 2) C…

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Q: In Exercises 9–11, find any intercepts and test for symmetry. The sketch the graphof the equation.9.…

A: (9) Given- y=4x-3 To find-  An intercepts and test for symmetry. The sketch the graph of the…

Q: Write the coordinates of the vertices after a reflection over the line y x. 10 8 6 41 21 -10 -8 -6…

A: topic - reflection  x and y coordinates of a point are interchanged after getting reflected through…

Q: 10. In the standard (x, y) coordinate plane, line r contains the points (6, 5) and (b,-5), and line…

A: Given problem is :

Q: What is the image of the triangle shown after a translation with the rule (x, y)→ (x-3, y+3)? 8 4 -4…

A: Given: The rule for the translation is x, y→x-3, y+3.

Q: What is the image of the point (2, 3) by reflection in the v-axis?a. (3, 2) b. (-2. 3) c. (2, -3) d.…

A: Given: The point is 2, 3. To determine: The image of the given point by reflection in the v-axis.

Q: What is the midpoint between the points A: (-3, -4) and B: (6, 1)?

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Q: Using the rule (x, y)-(-y, x) find the image points: A(2, 3) B(-5, 6) C(-1,-3) B'(, ) C(, ) A'(, )

A: 30. Using the rule (x,y)→(-y,x) Find the image pointsA(2,3)       B(-5,6)…

Q: 2. Suppose point P(4,-9) is translated according to the rule (x, y) - (x+ 3,y - 2). What are the…

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Q: Plot the points A(5, -2), B(-5, -2), C(5, 2), D(-5, 2), E(3, 0), and F(0, 3) on a coordinate plane.

A: To plot the points A(5,-2), B(-5,-2), C(5,2), D(-5,2), E(3,0), F(0,3)

Q: 6. The midpoint between the points A(-2,-3,1) and B(6,9, –3) is (b) (2,3, –1). (c) (-4, –6,2). (a)…

A: Midpoint of line joining (x1,y1,z1) and (x2,y2,z2) is  (x1+x22,y1+y22,z1+z22)

Q: Write the coordinates of the vertices after a reflection over the line y = -x. 104 8- 4 2 10 -8 9-…

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Q: 7) What are the coordinates of the vertex o y = -3(x+ 4)2 + 3? A) (-4,3) C) (4,3) D) (-4,-3) B)…

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Q: Which point is further from point P( 4, 5):     K( -3, 1)  or  N( 8, 7) ?

A: Given pointsP(4,5)K(-3,1)N(8,7)