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
Show that the points (a, a), (–a, –a) and (– √3 a, √3 a) are the vertices of an equilateral triangle. Also find its area.
Find the coordinates of the circumcentre of the triangle whose vertices are (8, 6), (8, – 2) and (2, – 2). Also, find its circum radius
Find the coordinates of the centre of the circle passing through the points (0, 0), (–2, 1) and (–3, 2). Also, find its radius.
Find the distance between the following pair of points:
(a+b, b+c) and (a-b, c-b)
Using the distance formula, show that the given points are collinear:
(6, 9), (0, 1) and (-6, -7)
Find the distance between the following pairs of point in the coordinate plane :
(4 , 1) and (-4 , 5)
KM is a straight line of 13 units If K has the coordinate (2, 5) and M has the coordinates (x, – 7) find the possible value of x.
Show that the point (0, 9) is equidistant from the points (– 4, 1) and (4, 1)
The points A(–1, –2), B(4, 3), C(2, 5) and D(–3, 0) in that order form a rectangle.
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.
