Advertisements
Advertisements
प्रश्न
The base QR of a n equilateral triangle PQR lies on x-axis. The coordinates of the point Q are (-4, 0) and origin is the midpoint of the base. Find the coordinates of the points P and R.
Advertisements
उत्तर
Let(x ,0) be the coordinates of R. Then
`0= (-4+x)/2 ⇒ x =4`
Thus, the coordinates of R are (4,0) . Here, PQ = QR = PR and the coordinates of P lies on . y - axis Let the coordinates of P be
(0,y) . Then ,
`PQ = QR ⇒ PQ^2 = QR^2`
`⇒ (0+4)^2 +(y-0)^2 = 8^2`
`⇒ y^2 = 64-16=48`
`⇒ y = +- 4 sqrt(3)`
`"Hence, the required coordinates are " R (4,0) and P (0,4 sqrt(3) ) or P (0, -4 sqrt(3) ).`
APPEARS IN
संबंधित प्रश्न
A (3, 2) and B (−2, 1) are two vertices of a triangle ABC whose centroid G has the coordinates `(5/3,-1/3)`Find the coordinates of the third vertex C of the triangle.
Find the equation of the perpendicular bisector of the line segment joining points (7, 1) and (3,5).
Determine the ratio in which the point P (m, 6) divides the join of A(−4, 3) and B(2, 8). Also, find the value of m.
Find the coordinates of the midpoints of the line segment joining
A(3,0) and B(-5, 4)
Find the area of quadrilateral PQRS whose vertices are P(-5, -3), Q(-4,-6),R(2, -3) and S(1,2).
Find the value of a, so that the point ( 3,a ) lies on the line represented by 2x - 3y =5 .
Show that A (−3, 2), B (−5, −5), C (2,−3), and D (4, 4) are the vertices of a rhombus.
Write the coordinates of the point dividing line segment joining points (2, 3) and (3, 4) internally in the ratio 1 : 5.
If the distance between the points (3, 0) and (0, y) is 5 units and y is positive. then what is the value of y?
If P (x, 6) is the mid-point of the line segment joining A (6, 5) and B (4, y), find y.
Find the area of triangle with vertices ( a, b+c) , (b, c+a) and (c, a+b).
If (−1, 2), (2, −1) and (3, 1) are any three vertices of a parallelogram, then
If A (5, 3), B (11, −5) and P (12, y) are the vertices of a right triangle right angled at P, then y=
If (x , 2), (−3, −4) and (7, −5) are collinear, then x =
Write the X-coordinate and Y-coordinate of point P(– 5, 4)
The line 3x + y – 9 = 0 divides the line joining the points (1, 3) and (2, 7) internally in the ratio ______.
The point whose ordinate is 4 and which lies on y-axis is ______.
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`.
