Question

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⚫ Math Class 10th
Co ordinate Geometry

➡ Question

Point A lies on the line segment PQ joining P (6, -6) and Q (-4, -1) in such a way that PA/PQ=2/5. If the point A also lies on the line 3x + k ( y+1)=0 , find K.

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Answer 1

Given P(6,-6) and Q(-4,-1).

Given PA : PQ = 2 : 5.

Let Point A(x,y) lie on PQ.

By External section formula:

x = (mx2 - nx1)/(m - n)

y = (my2 - ny1)/(m - n).

Here, (x1,y1) = (x,y) and (x2,y2) = (-4,-1) and (m,n) = (2,5).

Now,

$= > 6 =\frac{2(-4) - 5(x)}{2 - 5}$

= > (-3)(6) = 2(-4) - 5x

= > -18 = -8 - 5x

= > x = 2.

Similarly,

$= > -6 =\frac{2 * (-1) - 5 * y }{2 - 5}$

$= > -6(-3) = -2 - 5y$

$= > 18 = -2 - 5y$

$= > 18 + 2 = -5y$

$= > y = -4$

Therefore, the coordinates of point A(2,-4).

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Given that point A(2,-4) lies on the line 3x + k(y + 1) = 0

Substitute x = 2,y = -4, we get

= > 3(2) + k(-4 + 1) = 0

= > 6 + k(-3) = 0

= > 6 - 3k = 0

= > -3k = -6

= > k = 2.

Therefore, the value of k = 2.

Hope this helps!