The triangle whose vertices are (1,1), (5,3), and (4,5) is transformed by the rule (x,y) - (3x, 3y). Is the image similar or congruent to the original figure. Prove your answer.

Q: 2-) Find the Symmetric form of the equation of the line of in tersection of the two Planes X- +Z =2,…

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Q: A point on the a-axis that is equidistant from the points (9, – 6) |(- 8, 6) is and

A: the given points are .................first point .................second point now the third point…

Q: . Calculate the area of the triangle formed by the line 3x-7y+4 =0 , and the (ans.: 8/21) axes.

A: As per our guideline we are allowed to do 1 question at a time. Please post other questions next…

Q: Of all the points on the graph of z = 10 - x^2 - y^2 that lie above the plane x + 2y + 3z = 0, what…

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Q: The distance from (9,-6, 7) to yZ-plane is A9 O B. 6 OC. 166 OD. 85 O E.7

A: Distance of a point (a,b,c) from yz plane is as In yz plane x coordinate is zero and y= b and z= c.…

Q: Find the area of the triangle bounded by the lines y=x+3, y=2x-1 and y=-3x+4

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Q: The end points of line segment 4, which lies in the xy-plane, are (-2, 5) and (6,-3). Which of the…

A: i have used the formula of midpoint of the two points and the slope point form of the straight line…

Q: What is the vertex of y = Vx + 4+1 O (4, -1) O (4, 1) O (-4, 1) O (-4, -1)

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Q: Show that (km) is the number of paths in a square grid from (0,0) to the point (m,n) on the diagonal…

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Q: F = (-3y, 3x); R is the triangle with vertices (0, 0), (1, 0), and (0, 2).

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Q: Find the points on the cone 2² = x² + y² that are closest to the point (3,-3,0)

A: Cone Equation: z2=x2+y2 Given point: 3,-3,0 To find: the points on the cone nearest to the given…

Q: The line in R that is parallel to the y-axis and passes through the point (1, 2, 3) has equation + t…

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Q: Find b and c so that y 9x2 + bx + c has vertex (– 10, – 5). || - - b = C = ||

A: Given y=-9x2+bx+c and vertex(-10,-5) We have to find b ,c

Q: Find the condition for the points (a,0),(h,k),(0,b) when ais not equals to 0 to be collinear

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Q: Find the coordinates of the other point whose one end is (1,0) and its midpoint is (0,1)? O (1,-2) O…

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Q: , and mz = X+ 20 A (3x) 20 -2 =180 x+20)° What is the value of x? What is the image of the point…

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Q: Find the cartesian equation of the through (1, 3,-2) perpendicular to 51-71+3k. 5x-7y +3z - 22 0…

A: The required equation of the plane is : 5x - 7y + 3z + 22 = 0, which is the last option. The…

Q: For planes 2x + y - z = 2 and 2x + 3y + 5z = 4

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Q: Suppose that P is twice as far from (0, 0) as P is from (6, 0 Find such a point on the x-axis.

A: Let A0,0 and B6,0. It is given that P is twice as far from A0,0 as from B6,0. We know that if point…

Q: Consider a circle C in the xy-plane. If it is given that the points (2, 3),(2, −1) and (0, 3) are on…

A: Given points are (2, 3),(2, −1) and (0, 3)

Q: Find K so that the line through( 1, 5 )and( K, 8) is a) parallel to 4y -3X =7 and b) perpendicular…

A: compute the equation of a line joining (1,5) and (k,8) by using below formula.

Q: Find the points on x=3-y^2 that are closest to the given point (1,0)

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Q: Find the line of intersection of the given planes. 4x + y + z = 0 and 2x -y + 3z = 2

A: Given planes are: 4x + y + z = 0 2x - y + 3z = 0 Let us consider, z = t Then we get, 4x + y = -t 2x…

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: The point that is symmetric with respect to the y-axis to the point ( - 2, 5) is__________

A: It is known that the graph of y=fx is symmetric with respect to y-axis means f-x=fx=y.

Q: Find the point on the x-axis that is equidistant from the points (0,−1) and (5,−3)

A: To find the coordinates of the point satisfying the given conditions

Q: 3. [For students with ID # ending in 4 or 5.] Through the point (4, 2, -5) and perpendicular to the…

A: Here, the given equation of the plane is 3x+y-6z=8 So, the coefficients of x,y and z will give us…

Q: 2. Find the image of the line y = 5x + 7 under collineation a if a((x, y)) = (2у — х, х — 2).

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Q: Find the condition for the points (a,0) ,(h,k),(0,b) when ab is not equal to 0 to be collinear

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Q: Find the equation of the perpendicular bisector of th segment joining the points A(2, 3) and…

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Q: Suppose ABC- > LMN is a reflection across the line x = 0. If A(4, 4) what is the y coordinate of L?

A: Suppose ABC- > LMN is a reflection across the line x = 0. If A(4, 4) what is the y coordinate of…

Q: with the guldin's proposition 1 get the contents of the rotating object that occurs if the land…

A: As per the question we are given a 2d region bounded by the curve : y = 6 - 3x - x2 and the straight…

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A: y2-8xy-9x2=0 y2-9xy+xy+9y2=0y(y-9x)+x(y-9x)=0(x+y)(y-9x)=0 here we have two lines  L1:…

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

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Q: Find the relationship between x and y such that the point (x,y) is equidistance from the points…

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Q: If this trapezoid is moved through the translation (x+3, y-2), what will the coordinates of B' be?

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Q: What is the shortest distance from the point (4, 0, 5) to the sphere (x-1)2 + (y+2)2+2 = 367? %D O…

A: topic - shortest distance between point and sphere

Q: How can we recognize if the two planes were parallel or not

A: Consider the vector equation of the two given planes as, r→·n1→=d1r→·n2→=d2 Here, n1→ and n2→ are…

Q: 10. Is there any value of k that will make the planes kx + 2y-2kz + 3 = 0 and x-2ky + 5z = 0…

A: Two planes are perpendicular iff their normal vectors are orthogonal

Q: 1ol) 4 1. Are these two line segments parallel? 2 Nhy or why not? -10 -9 -B -7 6 -5 -4 -3 -2 -1 O 9…

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Q: 2. Find the equation of the line that is parallel to the intersection of planes 12, 2x-8y + z = 0…

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Q: show that points (2) ) are ( 3 ) 2 (52) A on-Coplaner ( ره ) -

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Q: B. If the two planes ax-4y - 9z = 4 and perpendicular. Find the value of a. x-2xy + 3z = 1 are

A: Topic = Geometry

Q: When the 2-D shape is completely drawn, how many points will be inside the 2-D shape?

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Q: the boat from its starting point?

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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: For planes 2x + y - z = 2 and 2x + 3y + 5z = 4.

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Q: Find b and c so that y 1x? + bx + c has vertex - (– 2, 0). С —

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Q: Find the dis tance from the Point (2,5) and the line 2y=6x-1

A: Given : To determine the distance of the point 2,5 and the line 2y = 6x-1