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

Q: Determine the geometric location of the points in R3 that equidistant from the plane y = 3 and the…

A: This is question of 3d geometry and locus.

Q: 2. (a) Show that the points (-2x, 5x), (0, 4x), (6x, x) are collinear.

A: Given that: (-2x, 5x), (0, 4x) , (6x, x)

Q: Write the coordinates of the vertices after a reflection over the line y = -5. 104 4 2. -10 -8 -9-…

A: Given query is to find the the cordinatea of vertices after reflection over y= -5.

Q: Find the perimeter of the triangle whose vertices are the following specified points in the plane.…

A: Given points are , (-4,9) , (-2,6), (3,-6)Let P =(-4,9)Q = 9-2,6)R = (3,-6)Hence peremeter = Length…

Q: 1. Quadrilateral ABCD with vertices A(-4, 1), B(-2, 3), C(0, -2), and D(-5, -2): k = 3 A'L B'( C'(L-…

A: We are given with the vertices of quadrilateral  and need to plot the graph.…

Q: Show that the points A(2, -1), B(1, 3), and C(-3, 2) are verticesof a square, and find the fourth…

A:

Q: Chas vertices A(1: 3): B(4: 1) and C(6: 4), Prove that

A:

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

A:

Q: Line AB is formed by the vertices A (1, 2, -2) and B (-1, 0, 2). If C is the midpoint of AB, find…

A: Given,  the coordinates of A and B which forms line AB  And c is the mid point is AB Hence the…

Q: Find b and c so that y = – 5z² + bz + c has vertex (9, 1). c =

A: The given equation y=-5x2+bx+c has a vertex at (9, 1). The given equation is an equation of a…

Q: Find the perimeter of the triangle whose vertices are the following specified points in the plane.…

A:

Q: R: square with vertices (0, 0), (2, 0), (0,

A: Given,         f(x, y)=19+3x-3y         R: square with vertices (0, 0), (2, 0), (0, 2), (2, 2).

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

A:

Q: do the points (-1,1) , (-3,5), and (0,8) form a tight triangle ?

A: We can check if the triangle formed by A, B, C is right triangle by two methods: 1) By checking if…

Q: find the value of y such that the points are collinear  (5,5) (-1,y) (2,4)

A: if three points are collinear then it means they cannot form a triangle so the area of triangle in…

Q: Prove that a quadrilateral with vertices J(2,-1), K(-1,-4), L(-4,-1), and M(-1,2) is a square.

A: We have to prove that the quadrilateral given is a Square

Q: Find the equation of the perpendicular bisector of side of the triangle having vertices A…

A: The triangle has vertices A (-1,-3),B(5,-3) and C(5,5) so to find the perpendicular bisectors let D,…

Q: Find the value of x and y in the rhombus. y° 3x 2x

A:

Q: Find the perimeter of the triangle with vertices A(-1, 2, 1), B(1, -1, 3), and C(3, 4, 5).

A: Given:The vertices A(-1, 2, 1), B(1, -1, 3), and C(3, 4, 5).The perimeter of the triangle is AB + BC…

Q: Find the perimeter of the triangle whose vertices are: 1. A(2,1), B(3, -5) and C(1, -3)

A: A(2, 1), B(3, -5) and C(1, -3)

Q: Show that the points (−1, 0), (3, 0), (1, 2), and (1, −2) are vertices of a square.

A: Let us consider A(-1,0) , B(3,0), C(1,2) and D(1,-2) To verify ABCD as a square We need to verify if…

Q: 2. What are the coordinates of the fourth vertex C so that rectangle ABCD is formed? Bty (-1,6) 81y…

A:

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

A:

Q: The ___________ is the point on a two-dimensionalplane from which the drops originated

A: The ___________ is the point on a two-dimensional plane from which the drops originated.

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

A:

Q: Find the peremiter of the trapezoid with these vertices (-2,-2),(-5,-2),(6,-5),(-5,-5)

A:

Q: A trapezoid has vertices located at the points: A(-2.3, 5), в(4.8, 5), с(4.8, —2.2), D(-2.3, –3.3).…

A: Use distance formula to find length            d=(x2-x1)2+(y2-y1)2

Q: Verify that parallelogram ABCD with vertices A(-5, – 1), B(-9, 6), C(-1, 5), and D(3, – 2) is a…

A: We can verify this as below using the diagonals.

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

A:

Q: 2. Triangle VWX with vertices -1, 0), W6, 8), and X(4,-3): (x, y) (x-1, y-5)

A: Given coordinates V(-1,0)W(6,8)X(4,-3)Given transformation :(x,y)→(x-1,y-5)

Q: Find b and c so that y=18x2+bx+c has vertex (9,−6)

A:

Q: 10. Quadrilateral ABCD with vertices A(-4, -1) B(0, -2), C(-1, -6), and (-6, -3) in the y-axis. A'(…

A:

Q: The vertices of a triangle are P(-3, 8), Q(-6, -4), and R(1, 1). What are the vertices of the image…

A: Given, the vertices of a triangle are P(-3, 8), Q(-6, -4), and R(1, 1)

Q: The base of a triangle passes through a fixed point (f,g) and its sides are bisected respectively at…

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: 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: Find the perimeter of the triangle with vertices at A(0,0) B(-3,-4) C(-5,0)

A: Perimeter of triangle = sun of all sides of a triangle.

Q: Find the perimeter of the triangle whose vertices are the following specified points in the plane.…

A:

Q: 50

A: Here given graph as Use the basic property of the rhombus 1.  The opposite angles of a rhombus are…

Q: 3. Mr. Cruz would like to buy a lot however, his broker gave the dimension of the lot using the…

A: The area of a quadrilateral when 4 of its vertices in counter-clockwise direction0 is:…

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

A:

Q: If two planes intersect, is it guaranteed that the method of setting one of the variables equal to…

A: Let say one the intersecting two planes is Ax + By + Cz =D When we put z = 0 the Plane reduces to…

Q: Find the point of intersection of the diagonals of the rhombus with vertices (-1, 2), (3, 4), (5,…

A: We know that diagonals of rhombus are perpendicular bisector of each other. Therefore Midpoint of…

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: A square has an area of 36 and one side that lies along the line y = 3. What could be the location…

A: To find the possible co-ordinates of square.

Q: Show that A(-4, – 1), B(0, –2), C(6, 1), and D(2, 2) are vertices of a parallelogram.

A: Given  A(-4,-1), B(0,-2), C(6,1) and D(2,2) To show: ABCD are vertices of a parallelogram.

Q: Fix one vertex at (0,a) in the (x,y)-plane and move another vertex along the x-axis. Show that the…

A: Given: A fixed vertex 0,a A second vertex moving along the x-axis. To show: The locus of the third…

Q: A trapezoid is a quadrilateral with at least one pair of parallel sides. Show that the quadrilateral…

A: slope of the line joining (x1,y1),(x2,y2)  is y2-y1x2-x1

Q: 9. Square ABCD with vertices A(-7, 5). B(-4, 7), C(-2, 4). and D(-5, 2): 90° counterclockwise

A: To graph the square with given points A,B,C,D.

Q: 2. AQRS with vertices Q(2, 5), R(7, 1), and S(-1, 2); translate by (-1, -2)

A: To find the coordinate of translate image we add vector and coordinate of original image.