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Let ABC be a right angled triangle such that medians through the vertices which are not right angled lie along the lines 2y=2x+5 and 6y=12x+5. if the length of the hypotenues is 12,then find the area of triangle ABC.

Let ABC be a right angled triangle such that medians through the vertices which are not right angled lie along the lines 2y=2x+5 and 6y=12x+5. if the length of the hypotenues is 12,then find the area of triangle ABC.

Grade:11

1 Answers

zyco zora69
26 Points
2 years ago
Let's say we have three points: r1 = (x1, y1), r2 = (x2, y2), r3 = (x3, y3). As we have six uknowns, we need six constraint equations.
Equations 1 and 2: (x1, y1) lies on the first line and (x2, y2) on the second.
Equations 3 and 4: the first line passes through (r1 + r3)/2, the second line passes through (r2 + r3)/2.
Equation 5: (r1 + r2 + r3)/3 is the same point as the intersection of the lines.
Equation 6: as the triangle is a right triangle, we need (r1 - r3)·(r2 - r3) = 0.
If so, we also have the length of the hypotenuse, so (r1 - r2)^2 = 144.

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