Advertisements
Advertisements
Question
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.
Advertisements
Solution
Let the y-coordinate of the point P be a.
Then, its x-coordinate will be 2a.
Thus, the coordinates of the point P are (2a, a).
t is given that the point P (2a, a) is equidistant from Q (2, −5) and R (−3, 6).
Thus, we have
`sqrt((2a-2)^2+(a-(-5)^2))=sqrt((2a-(-3)^2)+(a-6)^2)`
`=>sqrt((2a-2)^2+(a+5)^2)=sqrt((2a+3)^2+(a-6)^2)`
`sqrt(4a^2+4-8a+a^2+25+10a)=sqrt(4a^2+9+12a+a^2+36-12a)`
`=>sqrt(5a^2+2a+29)=sqrt(5a^2+45)`
Squaring both sides, we get
5a2+2a+29=5a2+45
⇒5a2+2a−5a2=45−29
⇒2a=16
⇒a=8
Thus, the coordinates of the point P are (16, 8), i.e. (2 × 8, 8).
APPEARS IN
RELATED QUESTIONS
If A(4, 3), B(-1, y) and C(3, 4) are the vertices of a right triangle ABC, right-angled at A, then find the value of y.
If two vertices of an equilateral triangle be (0, 0), (3, √3 ), find the third vertex
In a classroom, 4 friends are seated at the points A, B, C and D as shown in the following figure. Champa and Chameli walk into the class and after observing for a few minutes, Champa asks Chameli, “Don’t you think ABCD is a square?” Chameli disagrees.
Using distance formula, find which of them is correct.
Find x if distance between points L(x, 7) and M(1, 15) is 10.
Find the distance between the following point :
(p+q,p-q) and (p-q, p-q)
The distance between point P(2, 2) and Q(5, x) is 5 cm, then the value of x = ______.
Show that P(–2, 2), Q(2, 2) and R(2, 7) are vertices of a right angled triangle.
Show that A(1, 2), (1, 6), C(1 + 2`sqrt(3)`, 4) are vertices of an equilateral triangle.
|
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).
