Use the Distance Formula to determine the type of triangle that has these vertices: a) A(0, 0), B(4, 0), and C(2, 5) b) D(0, 0), E(4, 0), and F(2, 2V3) c) G(-5, 2), H(- 2, 6), and K(2, 3)

Q: Describe a method for determining whether four points P, Q , R , and S lie in the same plane?

A: We will show a method for determining whether four points P,Q,R and S lie in the same plane.

Q: Verify that the points are the vertices of a parallelogram, and find its area. A(1, 1, 3), B(-7, 5,…

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Q: Find the midpoint of the sides of the quadrilateral LOVE with vertices L(-3, -2), O (0, 6), V(4, 4),…

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Q: Show that the points (a,a),(-a,-a) and (-V3a, v3a) are the За vertice of an equilateral triangle.…

A: Given the co-ordinate of a triangle Let A=(a,a)B=(−a,−a)C=(−3a,3a)

Q: 2) Is a triangle with vertices G(3,2), H(8,5), and K(0,10) a right triangle? Justify

A: Let (x1,y1) and x2,y2 be two point ,then by distance formula distance between this point d =…

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

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Q: In a right triangle, with legs a and b and hypotenuse c, thePythagorean Theorem states that_________

A: It is given that, In a right triangle with a leg a and b and hypotenuse c.

Q: Sketch the translation of the triangle with the rule (x, y) → (x+5, y+1). T 5 -10 -5 5 10 --5

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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: II. Use coordinate geometry to prove that the diagonals of a rectangle. congruent. are

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Q: (b) Find the area of a triangle with the points A(1,0, 0), B(0,1,0), C(0,0, 1) as it vertices by…

A: (b) We have to find area of triangle with the points A1,0,0 , B0,1,0 and C0,0,1 by using cross…

Q: 1. Rhombus ABCD with vertices A(-3, -2), B(0, 3), C(5, 6), and D(2, 1): (x, y)- (x+2, y-6)

A: In Rhombus, A=(-3,-2)B=(0,3)C=(5,6)D=(2,1)

Q: What are the coordinates of the vertices of the triangle after the translation 2 units up?

A: For the translation 2 units up. The points on the graph change by  (x,y) goes to (x,y+2).

Q: What is the area of the triangle whose vertices are A(-1,2), B(3,-2),C(4,5)?

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Q: Find the perimeter of the triangle with vertices at​ A(0,0), B(−4​,−3​), and C(−5​,0).

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Q: A rectangle ABCD which measures 18 centimeters by 24 centimeters is folded once perpendicular to…

A: SOLUTION: Let ∠DCA=θ; tanθ=18/24=3/4 AC=18^2+24^2=30 Length of crease = AC*tanθ=30*(3/4)=22.5…

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

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Q: Use dot product to find the interior angles at A, B, and C of the triangle defined by the three…

A: HINT:  To calculate the angle we need the following thing: cos(α) = A.BAB We need to calculate AB…

Q: Find measures of the angles between the diagonals of the rectangle whose vertices are A = (1,0), B =…

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Q: Two vertices of an equilateral triangle are located at (2,0) and (-2,-3). What is the triangle's…

A: Distance between A(x1, y1) and B(x2, y2) is given by distance formula, AB =√((x2 - x1)² + (y2 - y1)²

Q: Use an algebraic proof to show that the points A(-3, 1), B(0, 4), C(0, 2), and D(-3, -1) form a…

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Q: The vertices of quadrilateral KAIT are K(0,0), A(a, 0), I(a + b, c), and T(b, c). Use coordinate…

A: Parallelogram is a kind of quadrilateral with two pairs of opposite sides. In a parallelogram, the…

Q: The coordinates at the vertices.A.B, and C of the triangle ABC are (-3,7), (2,19), and (10,7)…

A: Given,  The coordinates of vertices of triangle A-3, 7  B2, 19  C10, 7   We have to find the length…

Q: The coordinates at the vertices A.B, and C of the triangle ABC are (-3,7), (2,19), and (10,7)…

A: If we can find the height of the triangle then area can find out using 12×base×height

Q: Find the angle between in the two planes a = (1,2,3)and b =(4,-5,6)

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Q: On a coordinate plane, triangle FGH is formed with the vertices at point F(4, 2), point G(4, 6), and…

A: We have given that F(4, 2), G(4, 6) and H(6, 4).

Q: Find the area of a triangle with the points A(1,0,0), B(0,1,0), C(0,0, 1) as it vertices by using…

A: Question: Find the area of the triangle with the points A1,0,0, B0,1,0, C0,0,1 as its vertices by…

Q: Find the distance from the point A to the line through points B and C. Then show that the triangle…

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Q: Find the angle between in the two planes a = (1,2,3) and b =(4,-5,6)

A: Let's find angle between two plane.

Q: In a right triangle, with legs a and b and hypotenuse c, thePythagorean Theorem states that .

A: In a right triangle, with legs a and b and hypotenusec, the Pythagorean Theorem states  that______

Q: -20 -10 -20- 10- --10- -20- -30- (0, -16) 10 20

A: The distance between the points x1,y1 and x2,y2 is given by the distance formula: (x2-x1)2+(y2-y1)2…

Q: What is the area of the triangle ABC with vertices A(1,2,3), B(2, 4, 3), C(1,2, 0) ?

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Q: The points P(-1,0, 4), Q(1, 2, 4) and (0, -1, 3) are vertices of a right triangle.

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Q: Find the measures of the angles of the triangle whose vertices are A(1,0), B(2,1), and C(1,–2). 4.

A: Given : A(1,0) B(2,1) C(1,-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: 7. Find the measures of the hyperbolic angles of the Euclidean square with vertices (0, 1), (0, 2),…

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Q: А (2, 7) В (-1, 6) С (1, 1) D (4, 2)

A: Given points are A(2, 7), B(-1, 6), C(1,1) and D(4,2)

Q: The coordinates at the vertices A,B, and C of the triangle ABC are (-3,7), (2,19), and (10,7)…

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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 midpoint of each side of the triangle with vertices A (-5,4) B (3,6), c (2,2). Prove that…

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Q: Find the distance from the point A to the line through points B and C. Then show that the triangle…

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Q: Find the coordinates of the orthocenter of a triangle with vertices at each set of points on a…

A: Given that: (1, 5), (6, 10), (0, 16)

Q: The vertices of a quadrilateral are G(4, - 1), O(0, 0), L(2, 6), and D(6, 5). Show that…

A: Given: The vertices of a quadrilateral GOLD          G4,-1O0,0L2,6D6,5…

Q: Find the area of the triangle with vertices P(1, 6, –2), Q(0,0,0) and R(2,4, 1). - NOTE: Enter the…

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Q: Verify that the points are the vertices of a parallelogram, find its (section 9.7) area, and…

A: A(2,-1,4) B(3,1,2) C(0,5,6) D(-1,3,8)

Q: Transform the triangle with the rule (x,y)→(x+2,y-4)

A: From figure, it is clear that the points of the triangles are as given below (1,3),(2,1) and (5,4)

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: Let P be the parallelogram in the plane with vertices (0,0), (1,2), (1, 1), and (2, 3). Find SSp¤…

A: We need to find integral.

Q: The vertices of quadrilateral PQRS form a square P(0, 0), Q(4, 3), R(7, -1) and S(3, -4). Use…

A: locating the points on the graph we get

Q: A right triangle has vertices at A(3,0,2), B(4,3,0) and C(8,1, –1). At which vertex is the right…

A: We will find out the required solution.