10 Questions
What is the relationship between the Arithmetic Mean (A.M), Geometric Mean (G.M), and Harmonic Mean (H.M) as stated in the given text?
The text states that A.M ≥ G.M ≥ H.M.
What are the coordinates of the third vertex of a triangle if two of its vertices are (0, -4) and (6, 0), and the medians meet at the point (2, 0)?
The third vertex of the triangle is (2, -4).
What is the equation of the straight line that bisects the line segment joining the points (3, -4) and (1, 2) at a right angle?
The equation of the straight line is $y = (2/5)x + (8/5)$.
What is the equation of the ellipse whose center is at (0, 0), one vertex is at (0, -5), and one end of the minor axis is at (3, 0)?
The equation of the ellipse is $rac{x^2}{9} + rac{y^2}{25} = 1$.
Prove that the points (a, b, c), (b, c, a), and (c, b, a) form an equilateral triangle.
To prove that the points (a, b, c), (b, c, a), and (c, b, a) form an equilateral triangle, we need to show that the distances between any two of these points are equal.
Explain the relationship between the Arithmetic Mean (A.M), Geometric Mean (G.M), and Harmonic Mean (H.M) as stated in the given text.
The given text states that the relationship between the Arithmetic Mean (A.M), Geometric Mean (G.M), and Harmonic Mean (H.M) is: A.M ≥ G.M ≥ H.M.
Derive the equation of the straight line that bisects the line segment joining the points (3, -4) and (1, 2) at a right angle.
The equation of the straight line that bisects the line segment joining the points (3, -4) and (1, 2) at a right angle is $y = -rac{1}{3}x + rac{5}{3}$.
Write the equation of the ellipse whose center is at (0, 0), one vertex is at (0, -5), and one end of the minor axis is at (3, 0).
The equation of the ellipse is $rac{x^2}{9} + rac{y^2}{25} = 1$.
Prove that the points (a, b, c), (b, c, a), and (c, b, a) form an equilateral triangle.
To prove that the points (a, b, c), (b, c, a), and (c, b, a) form an equilateral triangle, we need to show that the distances between any two of these points are equal.
Find the coordinates of the third vertex of a triangle if two of its vertices are (0, -4) and (6, 0), and the medians meet at the point (2, 0).
The coordinates of the third vertex of the triangle are (4, 2).
Test your knowledge on coordinate geometry with questions involving finding the coordinate of a third vertex in a triangle, determining the equation of a line bisecting a line segment at right angles, identifying the equation of an ellipse, and proving points that form an equilateral triangle. Choose any three out of the given options to solve.
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