Advertisements
Advertisements
प्रश्न
The line segment joining the points A(2, 1) and B(5, −8) is trisected at the points P and Q such that P is nearer to A. If P also lies on the line given by 2x − y + k = 0, find the value of k.
उत्तर
We have two points A (2, 1) and B (5,−8). There are two points P and Q which trisect the line segment joining A and B.
Now according to the section formula if any point P divides a line segment joining A (x1, y1) and B (x2, y2) in the ratio m: n internally then,
`"P"("x", "y") = (("n""x"_1 + "m""x"_2)/("m" +"n") ,("n""y"_1 + "m""y"_2)/("m"+"n"))`
The point P is the point of trisection of the line segment AB. So, P divides AB in the ratio 1: 2
Now we will use section formula to find the coordinates of unknown point A as,
`"P"("x"_1, "y"_1) = ((1(5) + 2 (2))/(1 + 2), (2(1)+1(-8))/(1+2))`
= (3, -2)
Therefore, co-ordinates of point P is(3,−2)
It is given that point P lies on the line whose equation is
2x - y + k = 0
Since, point P satisfies this equation.
2(3) - (-2) + k = 0
So,
k = -8
संबंधित प्रश्न
Draw a triangle ABC with BC = 6 cm, AB = 5 cm and ∠ABC = 60°. Then construct a triangle whose sides are `3/4` of the corresponding sides of the ∆ABC.
Construct a ΔABC with BC = 7 cm, ∠B = 60° and AB = 6 cm. Construct another triangle whose sides are `3/4` times the corresponding sides of ΔABC
Construct a ΔABC in which AB = 6 cm, ∠A = 30° and ∠AB = 60° . Construct another ΔAB'C ' similar to ΔABC with base AB’ = 8 cm.
Construct a ΔABC in which BC = 8 cm, ∠B = 45° and ∠C = 60° . Construct another triangle similar to ΔABC such that its sides are `3/5`of the corresponding sides of ΔABC .
To construct a triangle similar to ΔABC in which BC = 4.5 cm, ∠B = 45° and ∠C =60° , using a scale factor of `3/7`, BC will be divided in the ratio
(a) 3 : 4 (b) 4 : 7 (c) 3 : 10 (d) 3 : 7
Draw a right triangle in which the sides (other than hypotenuse) are of lengths 4 cm and 3cm. Then, construct another triangle whose sides are `5/3`times the corresponding sides of the given triangle.
Draw a triangle ABC with BC = 7 cm, ∠ B = 45° and ∠C = 60°. Then construct another triangle, whose sides are `3/5` times the corresponding sides of ΔABC.
Construct a triangle with sides 5 cm, 5.5 cm and 6.5 cm. Now construct another triangle, whose sides are \[\frac{3}{5}\] times the corresponding sides of the given triangle.
Construct a triangle PQR with sides QR = 7 cm, PQ = 6 cm and \[\angle\]PQR = 60º. Then construct another triangle whose sides are \[\frac{3}{5}\] of the corresponiding sides of ∆PQR.
Draw a ∆ABC in which base BC = 6 cm, AB = 5 cm and ∠ABC = 60°. Then construct another triangle whose sides are \[\frac{3}{4}\] of the corresponding sides of ∆ABC.
