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Show that the points P(-1, -1), Q(2,3) a...

Show that the points P(-1, -1), Q(2,3) and R(2,6) are the vertices of a right-angled triangle.

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Using distance formula
`PQ^2=(2+1)^2+(3+1)^2=3^2+4^2=25`
`QR^2=(-2-2)^2+(6-3)^2=(-4)^2+3^2=25`
`PR^2=(-2+1)^2+(6+1)^2=(-1)^2+7^2=50`
`therefore PQ^2+QR^2=25+25=50=PR^2`
`implies DeltaPQR` is a right angle triangle (by converse Pythagoras theorem)
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MAHAVEER PUBLICATION-CARTESIAN AND POLAR COORDINATE SYSTEM-QUESTION BANK
  1. Find the distance between the points (5,3) and (-2,4)

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  2. Find a point on the xaxis, which is equidistant from the points (7,...

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  3. Find the distance between the points P(2,pi/2) and Q(3,pi/4) which are...

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  4. Convert the rectangular equation of a circle x^2+y^2=c^2 to a polar eq...

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  5. Prove that the diagonals of a rectangle are equal.

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  6. Show that the points P(-1, -1), Q(2,3) and R(2,6) are the vertices of ...

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  7. Show that the points A(1,2), B(4,5) and C(-1,0) lie on a straight line...

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  8. Find the distance between the following pair of points (5,4) and (2,-3...

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  9. Find the distance between the following pair of points (a,-a) and (b,b...

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  10. Plot the following polar coordinates: (3, (7pi)/4)

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  11. Plot the following polar coordinates: (-2, (5pi)/2)

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  12. Plot the following polar coordinates: (3,-pi/3)

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  13. Plot the following polar coordinates: (-3, -(3pi)/4)

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  14. Convert into polar coordinates: (-3,3)

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  15. Convert into polar coordinates: (0,6)

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  16. Convert into polar coordinates: (-1,sqrt3)

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  17. Convert into Cartesian coordinates: (6/sqrt2, pi/4)

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  18. Convert into Cartesian coordinates: ((sqrt2+1)/sqrt2,pi/4)

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  19. Convert into Cartesian coordinates: (2, 2pi)

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  20. Find the distance between the points P(3, (3pi)/6) and Q(-7, -pi/3) wh...

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