10. What is the midpoint of the longest side of the triangle with vertices A(1, 4), B(3, 4) and C(3, 6)? 6'

Q: Find the equation of the circle Busan bent X=y^2-y at point (0,1)

A: Given problem is : Find the equation of the circle Busan bent X=y^2-y at point (0,1) .

Q: In trapezoid ABCD (not shown), mZA = * + 50, and mZC = + 10, + 50. Find all possible mZB values of…

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Q: Show that the triangle with vertices (5, 4, −1), (3, 6, −1), and (3, 4, 1) is equilateral.

A: To show that the triangle with vertices 5, 4, -1, 3, 6, -1 and 3, 4, 1 is equilateral. Solution: Let…

Q: 7) Show that the triangle whose vertices are the points (1, 2, -1), (2, 3, 5) and (2, 1, 3) is/isn't…

A: Here we have to show that the triangle whose vertices are the points (1,2,-1), (2,3,5) and (2,1,3)…

Q: Find the perimeter of a triangle with vertices S(4,5), T(-2,-3) and W(5,-4).

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Q: Show that the points form the vertices of the polygon. right triangle: (0, 8), (4, 10), (6, 6)…

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Q: Consider a quadrilateral with vertices ܵS(-7, 2), Q(0.5, 3), R(3/2, -9/2), E(-6, -5.5) Determine…

A: The given question can be solved by using distance formula and the property of various types of…

Q: What is the midpoint of the segment AB given point A(-6,1) and point B(8,7)"

A: The midpoint of the line segment joining two points lies on the line segment. The coordinates of the…

Q: The distance between the points (a, b) and (c, d) is _____? So the distance between (3, 4) and (6,…

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Q: 4. Find the radius of this circle. -3- 2- 1- -8 -7 -6 -5 -4 -3 -2 -1 0 -1- O 6V5 O 2v2 O 3/2 O v2 5

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Q: Verify that the points are vertices of a parallelogram and find its area A(2,-3,1) B(6,5,-1)…

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Q: 2. Find the area of the triangle with vertices (0,0), (3,1) and (1,2)

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Q: 1. The vertices of quadrilateral ABCD are A(-2,3), B(4,6), C(10,3), and D(0,-2). Use coordinate…

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Q: 4. A point moves so that the sum of the squares of its distances from the faces of a cube is…

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Q: 10.) An equilateral triangular prism with all edges 4V3.

A: We know that, the surface area of an equilateral prism is, 2×3a24+3a×h where a is the side of the…

Q: 14) Write the equation of the perpendicular bisector of segment QR if Q(3, -2) and R(7, 6)

A: Find the equation

Q: 3. What are the new coordinates of line segment AC if the triangle is dilated using a scale factor…

A: What are the new coordinates of line segment AC if the triangle is dilated using a scale factor of…

Q: Find the of the triangle area with verfices Pl2,2,0), Q(13,-1) and R(-4,2,1)

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Q: Show that A(-3, 1), B(1, -1), C(4, 1), and D(3, 5) are vertices of a trapezoid.

A: Given vertices are A-3,1, B1,-1, C4,1 and D3,5. To show the vertices are of a trapezoid. Solution:…

Q: 5. Is the point (2, 7) on the circle defined by (x – 2) + (y – 7)2 = 4?

A: Given equation of the circle is: (x-2)2+(y-7)2=4 Given point is: (2,7) Substituting,x=2,y=7 in given…

Q: 2. Prove that the line joining the midpoint of a median to a vertex of the triangle trisects the…

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Q: What are the coordinates of the point on the directed line segment from (-8,-2) to (6, 2) that…

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Q: アon) usweris X10 बप्कणs In the ry-plane, what is the perimeter of an equilateral triangle with one…

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Q: (b) Determine the area of the triangle whose vertices are (1,1.2), (-1/2,0,2.5), and (3/3,2,3/2)by…

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Q: The distance between the points (a, b) and (c, d) is So the distance between (1, 2) and (7, 10) is

A: Given- The distance between the points a,b and c,d is a-c2+b-d2. To find- The distance between the…

Q: A trapezoid is shown in the coordinate plane. 10 9- 8 7- 6- 5- 4 3- 2- -10 -9 -8 -7 -6 -5 -4 -3 -2…

A: Given is a trapezoid, when we divide it into 2 parts   equally, the left and right side will be…

Q: 4. Find the area of the parallelogram with the points A(2,5, 6), B(4,8, 10), C(11, 7, 9) and D(9,4,…

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Q: What are the coordinates of the point on the directed line segment from (-9, –2) to (9, –6) that…

A: If a line segment, joined by x1,y1 and x2,y2, is internally divide by a point Qa,b in m:n ratio,…

Q: | 2. Find the radius of this circle. -2 -9 8 -7 -6 -5 -4 -3 -2 -1 0 -1- -2 -3 -4 -5 -6 O 8V5

A: Here, from the given graph: The center of the circle is at (-4,-2)

Q: Reflect the triangle over the line y=x with the rule (x,y)→(y,x) -8- 4- -8 -4 4 8 -4- --8

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Q: We are given 17 points inside a regular triangle of side length one. Prove that there are two points…

A: We use Pigeonhole Principle to solve this which states that if n items are put into m containers…

Q: 1. In the standard (x, y) coordinate plane, the endpoints of a segment are (2, 7) and (12, 19). What…

A: The endpoints are 2, 7 and 12, 19To find the x-coordinate of midpoint.

Q: If c>+, how many lines through the point (0, c) are normal lines to the parabola y = 3x2? normal…

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Q: The distance from (6,-7, 10) to yZ-plane is

A: Concepts let (x, y, z) be a point then  1) distance of the point from XY plane is…

Q: What is the distance from the point (1,9,3) to the xz-plane?

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Q: Drive the frenet frame ,curvature and torsion of binomial indicatrix of hypocycloid

A: We need to Derive the frenet frame, curvature and torsion of binomial indicatrix of hypocycloid

Q: 5. What are the (x, y) coordinates of the point where the terminal side of 0 circle? (ə) (-;-)

A: For unit circle, r = 1 x = r*cos(Q) y = r*sin(Q) Q = 4π/3

Q: The distance between the points  (a, b) and (c, d)  is         . So the distance between  (1, 2)…

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Q: Prove analytically that the midpoint of the hypotenuse of a right triangle is equidistant from the…

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Q: The triangle with vertices A(0, 1, 2), B(-1,0,2) and C(1,-2,0) has area = (ii)

A: A(0,1,2) B(-1,0,2) C(1,-2,0)

Q: Suppose  three points on a plane are defined as A=(8,2) B=(-1,-10) C=(-8,14) all lengths  are in…

A: Here we find the distance between the points and check the formation of the triangle.

Q: Construct three parallel lines so that the middle line is not equidistant fromthe other two. Then…

A: Let the three parallel lines be l, m, n and the equilateral triangle be ABC.

Q: calculate Sry³ dA where Ris the vertex of the triangle (0, 2), (1,1) and (3,3 )|

A: The sketch of R is

Q: 8 If the shaded square has center at C and an area of A, find C and A. 'y-axis C• (-4, 0) (0, 0)…

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Q: 2. If one of the vertices of the square circumscribing the circle|z – 1| = /2 is 2 + V3i. Find the…

A: Solution

Q: Show that the points form the vertices of the polygon. right triangle: (−4, 5), (0, 7), (2, 3)…

A: The given points are -4,5, 0,7, 2,3

Q: 9. What is the exact perimeter of a parallelogram with vertices at (3, 2), (4, 4), and (6, 1)?

A: To find Perimeter P?