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The coordinates of the vertex A of the t...

The coordinates of the vertex A of the triangle ABC are (-5,2) the equation of AC is `4x+3y+14=0` and the alttitude of the point A meets BC at the point D(3,-2). If `angle DAB=45^(@)`, find the equastion and gradient of AB, the coordinates of B and C and the ratio `BD:DC`.

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The correct Answer is:
Slope `=(1)/(3)` equation of `AB:x-3y+11=0 and B(7,6), C(1,-6), BD :DC=2:1` or slope `=-3`equation of `AB : 3x+y+13=0, B(-1,-10), C(1,-6) and BD:DC=2:1`.
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CHHAYA PUBLICATION-MISCELLANEOUS EXAMPLES-COORDINATE GEOMETRY (TWO DIMENSIONAL COORDINATE GEOMETRY)
  1. Show that the lines y=0, sqrt(3y)-xy=sqrt(3) and sqrt(3y)+x-10=0 form ...

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  2. Prove analytically that the perpendicular bisector of the sides of a t...

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  3. The coordinates of the vertex A of the triangle ABC are (-5,2) the equ...

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  4. The coordinates of the vertices of a triangle are [at(1)t(2),a(t(1)+t(...

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  5. Prove that diagonals of the parallelogram formed by the four straight ...

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  6. Find the locus of the foot of the perpendicular from the origin upon ...

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  7. Show that for all values of a,b and c the line (b-c)x+(c-a)y+a-b=0 alw...

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  8. Show that the locus of the point of intersection of the stright lines ...

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  9. Prove analytically that in any triangle the perpendiculars drawn from ...

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  10. Prove analytically that the bisectors of the interior angles of a tria...

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  11. If d(1),d(2),d(3) be the distances of a fixed point from the straight ...

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  12. Show that the quadrilateral formed by the four lines y=mx+a sqrt(a+m^(...

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  13. Show that the lines x cos alpha+ y alpha=p, x cos (alpha+ (2pi)/(3)) +...

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  14. 2x-y+4=0 is a diameter of a circle which circumscribes a rectangle ABC...

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  15. ABC is right-angle triangle, right -angled at A. The coordinates of B ...

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  16. The line through A( a cos theta,0) and perpendicular to the x-axis mee...

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  17. P and Q are two point on the line x-y+1=0, if O is the origin and bar...

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  18. O(0,0) and A(4,4) are two given points and B is any point. Find the eq...

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  19. Show that the image of the point (h,k) with respect to the striaight l...

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  20. A point moves so that sum of the squares of its distances from the ve...

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