Advertisements
Advertisements
प्रश्न
If the point A(0,2) is equidistant from the points B(3,p) and C(p, 5), find p.
Advertisements
उत्तर
The given ports are A(0,2) , B (3,p) and C (p,5).
`AB = AC ⇒ AB2 = AC2
` ⇒ (3-0)^2 +(P-2)^2= (P-0)^2 +(5-2)^2`
` ⇒9+P^2-4P+4=P^2+9`
⇒4 P = A ⇒ P=1
Hence , p =1.
APPEARS IN
संबंधित प्रश्न
Let ABCD be a square of side 2a. Find the coordinates of the vertices of this square when A coincides with the origin and AB and AD are along OX and OY respectively.
Find the points of trisection of the line segment joining the points:
5, −6 and (−7, 5),
Three consecutive vertices of a parallelogram are (-2,-1), (1, 0) and (4, 3). Find the fourth vertex.
Find the points on the y-axis which is equidistant form the points A(6,5) and B(- 4,3)
If p(x , y) is point equidistant from the points A(6, -1) and B(2,3) A , show that x – y = 3
Show that the following points are the vertices of a rectangle.
A (2, -2), B(14,10), C(11,13) and D(-1,1)
Find the area of the triangle formed by joining the midpoints of the sides of the triangle whose vertices are A(2,1) B(4,3) and C(2,5)
Find the value of a, so that the point ( 3,a ) lies on the line represented by 2x - 3y =5 .
The points \[A \left( x_1 , y_1 \right) , B\left( x_2 , y_2 \right) , C\left( x_3 , y_3 \right)\] are the vertices of ΔABC .
(i) The median from A meets BC at D . Find the coordinates of the point D.
(ii) Find the coordinates of the point P on AD such that AP : PD = 2 : 1.
(iii) Find the points of coordinates Q and R on medians BE and CF respectively such thatBQ : QE = 2 : 1 and CR : RF = 2 : 1.
(iv) What are the coordinates of the centropid of the triangle ABC ?
Find the values of x for which the distance between the point P(2, −3), and Q (x, 5) is 10.
The line segment joining points (−3, −4), and (1, −2) is divided by y-axis in the ratio.
If the centroid of the triangle formed by the points (a, b), (b, c) and (c, a) is at the origin, then a3 + b3 + c3 =
If the points P (x, y) is equidistant from A (5, 1) and B (−1, 5), then
The line segment joining the points A(2, 1) and B (5, - 8) is trisected at the points P and Q such that P is nearer to A. If P also lies on the line given by 2x - y + k= 0 find the value of k.
In the above figure, seg PA, seg QB and RC are perpendicular to seg AC. From the information given in the figure, prove that: `1/x + 1/y = 1/z`
The line 3x + y – 9 = 0 divides the line joining the points (1, 3) and (2, 7) internally in the ratio ______.
Point (–10, 0) lies ______.
Abscissa of all the points on the x-axis is ______.
Abscissa of a point is positive in ______.
If the points P(1, 2), Q(0, 0) and R(x, y) are collinear, then find the relation between x and y.
Given points are P(1, 2), Q(0, 0) and R(x, y).
The given points are collinear, so the area of the triangle formed by them is `square`.
∴ `1/2 |x_1(y_2 - y_3) + x_2(y_3 - y_1) + x_3(y_1 - y_2)| = square`
`1/2 |1(square) + 0(square) + x(square)| = square`
`square + square + square` = 0
`square + square` = 0
`square = square`
Hence, the relation between x and y is `square`.
