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.
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
Find the value of k, if the point P (0, 2) is equidistant from (3, k) and (k, 5).
Prove that the points (3, 0), (4, 5), (-1, 4) and (-2, -1), taken in order, form a rhombus.
Also, find its area.
Find the coordinates of the point which divides the line segment joining (−1,3) and (4, −7) internally in the ratio 3 : 4
Prove that (4, 3), (6, 4) (5, 6) and (3, 5) are the angular points of a square.
Find the area of a quadrilateral ABCD whose vertices area A(3, -1), B(9, -5) C(14, 0) and D(9, 19).
The abscissa of a point is positive in the
The area of the triangle formed by the points P (0, 1), Q (0, 5) and R (3, 4) is
Show that the points (−4, −1), (−2, −4) (4, 0) and (2, 3) are the vertices points of a rectangle.
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 area of a parallelogram ABCD if three of its vertices are A(2, 4), B(2 + \[\sqrt{3}\] , 5) and C(2, 6).
If \[D\left( - \frac{1}{5}, \frac{5}{2} \right), E(7, 3) \text{ and } F\left( \frac{7}{2}, \frac{7}{2} \right)\] are the mid-points of sides of \[∆ ABC\] , find the area of \[∆ ABC\] .
Write the perimeter of the triangle formed by the points O (0, 0), A (a, 0) and B (0, b).
Write the coordinates the reflections of points (3, 5) in X and Y -axes.
Write the ratio in which the line segment doining the points A (3, −6), and B (5, 3) is divided by X-axis.
The distance between the points (a cos θ + b sin θ, 0) and (0, a sin θ − b cos θ) is
The coordinates of the point on X-axis which are equidistant from the points (−3, 4) and (2, 5) are
The coordinates of the fourth vertex of the rectangle formed by the points (0, 0), (2, 0), (0, 3) are
Signs of the abscissa and ordinate of a point in the second quadrant are respectively.
The points (–5, 2) and (2, –5) lie in the ______.
The distance of the point (–6, 8) from x-axis is ______.
