1. Let 21, 22, 23 denote the vertices of an equilateral triangle. Prove that 2₁ +2²² +2²=2122 +2223 +2371. 2. Show that the transformation I(z) = or a circle. sends a circle to a straight line

Q: Q2. Use a scalar product the check whether the points A (0, 4, 1), B(2, 3, -1), C(4, 5, 0) and D(2,…

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Q: All parallelogram are squares  •True  •False

A: To Determine:  Is the statement is True or False All parallelogram are squares

Q: Find the image of a triangle whose vertices are A(2, 4), B(4, 2), and C(6, 8) under a dilation with…

A: Given  A(2,4), B(4,2)  and C6,8 Given dilation factor 12 where the origin is the center Therefore…

Q: Find the area of triangle with (1,-1,-2), (-2,0,-1) and (0,-2,1) as vertices?

A: Given: 1,-1,-2, -2,0,-1  and 0,-2,1

Q: Without plotting the points or drawing the figure, find the coordinates of the new vertices of the…

A: given pentagon with vertices at V(3,2), W(5,10), X(6,12), Y(−0.5,1.25), Z(1,0)

Q: Is the triangle with the vertices M(-2,5), N(12,3), Q(10,-11) a right triangle?

A: Solved below

Q: Prove that the point 2a +b-c, 5a -b+ 2c and 8a – 3b+5c are collinear.

A: Given, 3 vectors or points, A(2,1,-1) B(5,-1,2) C(8,-3,5)

Q: What are the projections of the point (−2, 3, 4) on the xy-, xz-, and yz-planes? Draw a picture and…

A: Given, the point (-2, 3, 4), we have to find the projections of this point on the xy-, yz-, and…

Q: Triangle ABC is defined in the coordinate plane by the points A = (1,1), B = (3, 4), and C (4, 2),…

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Q: 2. Write the symmetric equation of a line through the points (0, 2,8) and (3,-3, 4). Find where this…

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Q: Imagine a triangle △ABC where A(−53,−60,−49), B(−102,−98,−107), and C(3,6,5) is in 3D space. A point…

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Q: The vertices of APQR are P(0, 0), Q(- 6, 0), and R(-6, 6). Find the area of APQR.

A: Given:

Q: Use the Conjugate Pairs Theorem

A: Given: Use the Conjugate Pairs Theorem

Q: ³√ √ ₁ (5₂ of (5x + 4y)dA where R is the parallelogram with vertices (0,0), (2,-5), (-3,-2), and…

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Q: Prove that the points (-2, -1), (1, 0), (4, 3), and (1, 2) are the vertices of a parallelogram. Is…

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Q: The vertices of a triangle are (2, 3), (-4, 6), and (2, -6) 1. Determine the ordinate of the…

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Q: The triangle with vertices congruent to the triangle

A: The vertices of triangle are A(0, 0), B(2,1) and C(0,5).  The vertices of other triangle are P(2,…

Q: Find the vertices and the area of the triangle formed by the graphs of y=|x-3| and -x+2y=5?

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Q: The points (3, 0), (-1, 1), (5, 1) and (1, 2) are the vertices of a parallelogram ABC D. If ABCD is…

A: new point after translation are A' = A + v = (3,0) +(3,-2) = (3+3 , 0-2) = (6,-2) B'= B + v =…

Q: Prove that cyclic parallelogram is a rectangle.

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