Advertisements
Advertisements
प्रश्न
Find the co-ordinates of the point equidistant from three given points A(5,3), B(5, -5) and C(1,- 5).
Advertisements
उत्तर
Let the required point be P (x, y). Then AP = BP = CP
That is, `(AP)^2 = (BP)^2 = (cp)^2`
This means`(Ap)^2 = (BP)^2`
`⇒(x-5)^2 +(y-3)^2 = (x-5)^2 +(y+5)^2`
`⇒x^2-10x+25+y^2-6y +9 =x^2-10x +25+y^2 +10y+25`
`⇒x^2 -10x +y^2 -6y +34 =x^2 - 10x+y^2+10y+50`
`⇒x^2-10x +y^2-6y-x^2 +10x-y^2-10y = 50-34`
⇒ -16y=16
`⇒y=-16/16=-1`
And `(BP)^2 = (CP)^2`
`⇒(x-5)^2 +(y+5)^2 = (x-1)^2 +(y+5)^2`
`⇒ x^2 -10x +25 +y^2 +10y +25 = x^2 -2x +1 +y^2 +10y +25`
`⇒ x^2 -10x +y^2 +10y + 50= x^2 -2x +y^2 +10y +26`
`⇒x^2 -10x +y^2 +10y -x^2 +2x - y^2 -10y = 26-50`
⇒ -8x = -24
`⇒ x = (-24)/(-8) = 3`
Hence, the required point is (3, -1 ).
APPEARS IN
संबंधित प्रश्न
If A(–2, 1), B(a, 0), C(4, b) and D(1, 2) are the vertices of a parallelogram ABCD, find the values of a and b. Hence find the lengths of its sides
Find a point on the x-axis which is equidistant from the points (7, 6) and (−3, 4).
Find the value of x such that PQ = QR where the coordinates of P, Q and R are (6, -1), (1, 3) and (x, 8) respectively.
Prove that the points (0, 0), (5, 5) and (-5, 5) are the vertices of a right isosceles triangle.
Find a point on y-axis which is equidistant from the points (5, -2) and (-3, 2).
Show that the following points are the vertices of a square:
A (0,-2), B(3,1), C(0,4) and D(-3,1)
Find the centroid of ΔABC whose vertices are A(2,2) , B (-4,-4) and C (5,-8).
If the point \[C \left( - 1, 2 \right)\] divides internally the line segment joining the points A (2, 5) and B( x, y ) in the ratio 3 : 4 , find the value of x2 + y2 .
If the point P (m, 3) lies on the line segment joining the points \[A\left( - \frac{2}{5}, 6 \right)\] and B (2, 8), find the value of m.
If three points (x1, y1) (x2, y2), (x3, y3) lie on the same line, prove that \[\frac{y_2 - y_3}{x_2 x_3} + \frac{y_3 - y_1}{x_3 x_1} + \frac{y_1 - y_2}{x_1 x_2} = 0\]
Write the coordinates the reflections of points (3, 5) in X and Y -axes.
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 the distance between the points (4, p) and (1, 0) is 5, then p =
If A (5, 3), B (11, −5) and P (12, y) are the vertices of a right triangle right angled at P, then y=
The coordinates of the fourth vertex of the rectangle formed by the points (0, 0), (2, 0), (0, 3) are
If the line segment joining the points (3, −4), and (1, 2) is trisected at points P (a, −2) and Q \[\left( \frac{5}{3}, b \right)\] , Then,
What is the nature of the line which includes the points (-5, 5), (6, 5), (-3, 5), (0, 5)?
Students of a school are standing in rows and columns in their playground for a drill practice. A, B, C and D are the positions of four students as shown in figure. Is it possible to place Jaspal in the drill in such a way that he is equidistant from each of the four students A, B, C and D? If so, what should be his position?
The point whose ordinate is 4 and which lies on y-axis is ______.
Statement A (Assertion): If the coordinates of the mid-points of the sides AB and AC of ∆ABC are D(3, 5) and E(–3, –3) respectively, then BC = 20 units.
Statement R (Reason): The line joining the mid-points of two sides of a triangle is parallel to the third side and equal to half of it.
