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If two vertices of a triangle are (1,3) and (4,-1) and the area of triangle is 5 sq. units, then the angle at the third vertex lies in :

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The correct Answer is:
A
Length of base `AB=5`
`therefore` Length of altitude `CM=2`
(`therefore` Area is 5sq.units)
Max. `angleACB=2tan^(-1).(5)/(4)`
`therefore" "angleACBin(0,2tan^(-1).(5)/(4)]`
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CENGAGE PUBLICATION-COORDINATE SYSYEM -Exercises
  1. A B C is an isosceles triangle. If the coordinates of the base are B(1...

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  2. If two vertices of a triangle are (1,3) and (4,-1) and the area of tri...

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  3. Which of the following sets of points form an equilateral triangle? (...

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  4. A particle p moves from the point A(0,4) to the point 10 ,-4) . The pa...

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  5. If |x1y1 1x2y2 1x3y3 1|=|a1b1 1a2b2 1a3b3 1| then the two triangles ...

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  6. O P Q R is a square and M ,N are the middle points of the sides P Qa n...

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  7. A straight line passing through P(3,1) meets the coordinate axes at Aa...

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  8. Let A-=(3,-4),B-=(1,2)dot Let P-=(2k-1,2k+1) be a variable point such ...

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  9. The polar coordinates equivalent to (-3,sqrt3) are

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  10. If the point P[X1+t(X2-X1),y1+t(y2-y1] divides AB internally where (X1...

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  11. P and Q are points on the line joining A(-2,5) and B(3,1) such that A ...

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  12. In triangle ABC, angle B is right angled, AC=2 and A(2,2), B(1,3) then...

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  13. One vertex of an equilateral triangle is (2,2) and its centroid is (-2...

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  14. ABCD is a rectangle with A(-1,2),B(3,7) and AB:BC=4:3. If P is the cen...

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  15. If (2,-3), (6,5) and (-2,1) are three consecutive vertices of a rhombu...

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  16. If poitns A(3,5) and B are equidistant from H(sqrt2,sqrt5) and B has r...

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  17. Let n be the number of points having rational coordinates equidistant...

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  18. In a triangle ABC the sides BC=5, CA=4 and AB=3. If A(0,0) and the int...

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  19. If A(0, 0), B(1, 0) and C(1/2,sqrt(3)/2) then the centre of the circle...

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  20. Statement 1: If in a triangle, orthocentre, circumcentre and centroid ...

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