Advertisements
Advertisements
प्रश्न
Find value of x for which the distance between the points P(x,4) and Q(9,10) is 10 units.
उत्तर
The given points are `P (x,4) and Q (9,10)
`∴ PQ = sqrt((x-9)^2 +(4-10)^2)`
`=sqrt((x-9)^2 +(-6)^2)`
`=sqrt(x^2 -18x+81+36)`
`=sqrt(x^2-18x+117)`
∵ PQ = 10
`∴ sqrt(x^2 -18x +117)`
`⇒x^2 -18x +117=100` (Squaring both sides)
` ⇒ x^2 -18x +17 `
`x^2 -17x -x +17=0`
⇒ ( x - 17 ) ( x - 1) = 0
⇒ ( x - 17 ) (x - 1 ) = 0
⇒ x- 17 = 0 or x - 1 = 0
⇒ x = 17 or x = 1
Hence, the values of x are 1 and 17.
APPEARS IN
संबंधित प्रश्न
Name the type of quadrilateral formed, if any, by the following point, and give reasons for your answer:
(−3, 5), (3, 1), (0, 3), (−1, −4)
If the point P(x, y ) is equidistant from the points A(5, 1) and B (1, 5), prove that x = y.
`" Find the distance between the points" A ((-8)/5,2) and B (2/5,2)`
Find the distance of the following point from the origin :
(8 , 15)
Find the distance between the origin and the point:
(-8, 6)
A point P lies on the x-axis and another point Q lies on the y-axis.
If the abscissa of point P is -12 and the ordinate of point Q is -16; calculate the length of line segment PQ.
Find distance between point A(7, 5) and B(2, 5)
Find distance between point Q(3, – 7) and point R(3, 3)
Solution: Suppose Q(x1, y1) and point R(x2, y2)
x1 = 3, y1 = – 7 and x2 = 3, y2 = 3
Using distance formula,
d(Q, R) = `sqrt(square)`
∴ d(Q, R) = `sqrt(square - 100)`
∴ d(Q, R) = `sqrt(square)`
∴ d(Q, R) = `square`
Points A(4, 3), B(6, 4), C(5, –6) and D(–3, 5) are the vertices of a parallelogram.
Read the following passage:
|
Alia and Shagun are friends living on the same street in Patel Nagar. Shagun's house is at the intersection of one street with another street on which there is a library. They both study in the same school and that is not far from Shagun's house. Suppose the school is situated at the point O, i.e., the origin, Alia's house is at A. Shagun's house is at B and library is at C. |
Based on the above information, answer the following questions.
- How far is Alia's house from Shagun's house?
- How far is the library from Shagun's house?
- Show that for Shagun, school is farther compared to Alia's house and library.
OR
Show that Alia’s house, shagun’s house and library for an isosceles right triangle.
