Advertisements
Advertisements
Question
Find the points on the x-axis which are at a distance of `2sqrt(5)` from the point (7, – 4). How many such points are there?
Solution
We know that, every point on the x-axis in the form (x, 0).
Let P(x, 0) the point on the x-axis have `2sqrt(5)` distance from the point Q(7, – 4).
By given condition,
PQ = `2sqrt(5)` ...`[∵ "Distance formula" = sqrt((x_2 - x_1)^2 + (y_2 - y_1)^2)]`
⇒ (PQ)2 = 4 × 5
⇒ (x – 7)2 + (0 + 4)2 = 20
⇒ x2 + 49 – 14x + 16 = 20
⇒ x2 – 14x + 65 – 20 = 0
⇒ x2 – 14x + 45 = 0
⇒ x2 – 9x – 5x + 45 = 0 ...[By factorisation method]
⇒ x(x – 9) – 5(x – 9) = 0
⇒ (x – 9)(x – 5) = 0
∴ x = 5, 9
Hence, there are two points lies on the axis, which are (5, 0) and (9, 0), have `2sqrt(5)` distance from the point (7, – 4).
APPEARS IN
RELATED QUESTIONS
Find the value of x, if the distance between the points (x, – 1) and (3, 2) is 5.
Show that four points (0, – 1), (6, 7), (–2, 3) and (8, 3) are the vertices of a rectangle. Also, find its area
If Q (0, 1) is equidistant from P (5, − 3) and R (x, 6), find the values of x. Also find the distance QR and PR.
Find the distance between the points
P(a + b,a - b)andQ(a -b,a + b)
Find the value of y for which the distance between the points A (3, −1) and B (11, y) is 10 units.
Find the coordinate of O , the centre of a circle passing through A (8 , 12) , B (11 , 3), and C (0 , 14). Also , find its radius.
Prove that the points (6 , -1) , (5 , 8) and (1 , 3) are the vertices of an isosceles triangle.
Show that the points (2, 0), (–2, 0), and (0, 2) are the vertices of a triangle. Also, a state with the reason for the type of triangle.
Show that the point (0, 9) is equidistant from the points (– 4, 1) and (4, 1)
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.
