Advertisements
Advertisements
प्रश्न
If the distance between the points (4, P) and (1, 0) is 5, then the value of p is ______.
पर्याय
4 only
± 4
– 4 only
0
Advertisements
उत्तर
If the distance between the points (4, p) and (1, 0) is 5, then the value of p is ± 4.
Explanation:
According to the question,
The distance between the points (4, p) and (1, 0) = 5
d = `sqrt((x_2 - x_1)^2 + (y_2 - y_1)^2`
i.e., `sqrt((1 - 4)^2 + (0 - "p")^2` = 5
⇒ `sqrt((-3)^2 + "p"^2)` = 5
⇒ `sqrt(9 + "p"^2)` = 5
On squaring both the sides, we get
9 + p2 = 25
⇒ p2 = 16
⇒ p = ± 4
Hence, the required value of p is ± 4.
APPEARS IN
संबंधित प्रश्न
The x-coordinate of a point P is twice its y-coordinate. If P is equidistant from Q(2, –5) and R(–3, 6), find the coordinates of P.
If the point (x, y) is equidistant from the points (a + b, b – a) and (a – b, a + b), prove that bx = ay.
Find the coordinates of the circumcentre of the triangle whose vertices are (8, 6), (8, – 2) and (2, – 2). Also, find its circum radius
Check whether (5, -2), (6, 4) and (7, -2) are the vertices of an isosceles triangle.
Name the type of quadrilateral formed, if any, by the following points, and give reasons for your answer:
(- 1, - 2), (1, 0), (- 1, 2), (- 3, 0)
Find the distance between the points
P(a sin ∝,a cos ∝ )and Q( acos ∝ ,- asin ∝)
Find the distance between the following pairs of point.
W `((- 7)/2 , 4)`, X (11, 4)
Find the distance between the following pair of point in the coordinate plane.
(1 , 3) and (3 , 9)
Find the distance of the following point from the origin :
(13 , 0)
Find the distance between the following point :
(sin θ , cos θ) and (cos θ , - sin θ)
Find the value of a if the distance between the points (5 , a) and (1 , 5) is 5 units .
Prove that the points (a, b), (a + 3, b + 4), (a − 1, b + 7) and (a − 4, b + 3) are the vertices of a parallelogram.
Find the distance between the following pairs of points:
`(3/5,2) and (-(1)/(5),1(2)/(5))`
Find the coordinates of the points on the y-axis, which are at a distance of 10 units from the point (-8, 4).
The point which lies on the perpendicular bisector of the line segment joining the points A(–2, –5) and B(2, 5) is ______.
Ayush starts walking from his house to office. Instead of going to the office directly, he goes to a bank first, from there to his daughter’s school and then reaches the office. What is the extra distance travelled by Ayush in reaching his office? (Assume that all distances covered are in straight lines). If the house is situated at (2, 4), bank at (5, 8), school at (13, 14) and office at (13, 26) and coordinates are in km.
If (a, b) is the mid-point of the line segment joining the points A(10, –6) and B(k, 4) and a – 2b = 18, find the value of k and the distance AB.
The centre of a circle is (2a, a – 7). Find the values of a if the circle passes through the point (11, – 9) and has diameter `10sqrt(2)` units.
|
In a GPS, The lines that run east-west are known as lines of latitude, and the lines running north-south are known as lines of longitude. The latitude and the longitude of a place are its coordinates and the distance formula is used to find the distance between two places. The distance between two parallel lines is approximately 150 km. A family from Uttar Pradesh planned a round trip from Lucknow (L) to Puri (P) via Bhuj (B) and Nashik (N) as shown in the given figure below.
|
Based on the above information answer the following questions using the coordinate geometry.
- Find the distance between Lucknow (L) to Bhuj (B).
- If Kota (K), internally divide the line segment joining Lucknow (L) to Bhuj (B) into 3 : 2 then find the coordinate of Kota (K).
- Name the type of triangle formed by the places Lucknow (L), Nashik (N) and Puri (P)
[OR]
Find a place (point) on the longitude (y-axis) which is equidistant from the points Lucknow (L) and Puri (P).
Find the distance between the points O(0, 0) and P(3, 4).
