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
How will you describe the position of a table lamp on your study table to another person?
If the points A(k + 1, 2k), B(3k, 2k + 3) and C(5k − 1, 5k) are collinear, then find the value of k
If G be the centroid of a triangle ABC, prove that:
AB2 + BC2 + CA2 = 3 (GA2 + GB2 + GC2)
Show that the points A(5, 6), B(1, 5), C(2, 1) and D(6,2) are the vertices of a square.
In what ratio is the line segment joining the points (-2,-3) and (3, 7) divided by the y-axis? Also, find the coordinates of the point of division.
If three consecutive vertices of a parallelogram are (1, -2), (3, 6) and (5, 10), find its fourth vertex.
In what ratio does the point (−4, 6) divide the line segment joining the points A(−6, 10) and B(3,−8)?
If the point C(k,4) divides the join of A(2,6) and B(5,1) in the ratio 2:3 then find the value of k.
The co-ordinates of point A and B are 4 and -8 respectively. Find d(A, B).
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 \[D\left( - \frac{1}{5}, \frac{5}{2} \right), E(7, 3) \text{ and } F\left( \frac{7}{2}, \frac{7}{2} \right)\] are the mid-points of sides of \[∆ ABC\] , find the area of \[∆ ABC\] .
If the mid-point of the segment joining A (x, y + 1) and B (x + 1, y + 2) is C \[\left( \frac{3}{2}, \frac{5}{2} \right)\] , find x, y.
The point on the x-axis which is equidistant from points (−1, 0) and (5, 0) is
Any point on the line y = x is of the form ______.
Point P(– 4, 2) lies on the line segment joining the points A(– 4, 6) and B(– 4, – 6).
Point (3, 0) lies in the first quadrant.
Co-ordinates of origin are ______.
Assertion (A): Mid-point of a line segment divides the line segment in the ratio 1 : 1
Reason (R): The ratio in which the point (−3, k) divides the line segment joining the points (− 5, 4) and (− 2, 3) is 1 : 2.
