Question 19: If two vertices of an equilateral triangle be (0,0) and (3, ), find the third vertex using distance formula.

Question

KnowledgeBoat · Accepted Answer

Given, A = (0, 0) B =(3, ) Distance between the given points = Length of AB: Let the third vertex be C(x, y) Since the triangle is equilateral, the distance from C to A and C to B must also be . Length of AC = Length of AB Length of BC = Length of AB Substitute the value of y in equation (1), x2 + ((2 - x))2 = 12 x2 + 3(4 - 4x + x2) = 12 x2 + 12 - 12x + 3x2 = 12 4x2 - 12x = 0 4x(x - 3) = 0 ∴ x = 0 or x = 3 If x = 0, then y = Vertex C = (0, ) If x = 3, then y = Vertex C = (3, ). Hence, third vertex = (0, ) and (3, ).

Mathematics

Question 19: If two vertices of an equilateral triangle be (0,0) and (3, ), find the third vertex using distance formula.

Distance Formula

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Mathematics

Question 19: If two vertices of an equilateral triangle be (0,0) and (3, ), find the third vertex using distance formula.

Distance Formula

Related Questions

The distances of point P(x, y) from the points A(1, -3) and B(-2, 2) are in the ratio 2 : 3.Show that : 5x2 + 5y2 - 34x + 70y + 58 = 0.

The points A(3, 0), B(a, -2) and C(4, -1) are the vertices of triangle ABC right-angled at vertex A. Find the value of a.

The distances of point P(x, y) from the points A(1, -3) and B(-2, 2) are in the ratio 2 : 3.
Show that : 5x² + 5y² - 34x + 70y + 58 = 0.