Advertisements
Advertisements
प्रश्न
Show that the point (11, – 2) is equidistant from (4, – 3) and (6, 3)
Advertisements
उत्तर
Let P(x1, y1) = P(11, – 2), Q(x2, y2) = Q(4, – 3), R(x3, y3) = R(6, 3)
By distance formula,
d(P, Q) = `sqrt((x_2 - x_1)^2 + (y_2 - y_1)^2`
= `sqrt((4 - 11)^2 + [-3 - (-2)]^2`
= `sqrt((-7)^2 + (-1)^2`
= `sqrt(49 + 1)`
= `sqrt(50)`
= `5sqrt(2)`
And
d(P, R) = `sqrt((x_3 - x_1)^2 + (y_3 - y_1)^2`
= `sqrt((6 - 11)^2 + [3 - (-2)]^2`
= `sqrt((-5)^2 + (5)^2`
= `sqrt(25 + 25)`
= `sqrt(50)`
= `5sqrt(2)`
Here, d(P, Q) = d(P, R)
∴ Point (11, – 2) is equidistant from (4, – 3) and (6, 3).
APPEARS IN
संबंधित प्रश्न
If the point P(x, y) is equidistant from the points A(a + b, b – a) and B(a – b, a + b). Prove that bx = ay.
If P and Q are two points whose coordinates are (at2 ,2at) and (a/t2 , 2a/t) respectively and S is the point (a, 0). Show that `\frac{1}{SP}+\frac{1}{SQ}` is independent of t.
In a classroom, 4 friends are seated at the points A, B, C and D as shown in the following figure. Champa and Chameli walk into the class and after observing for a few minutes, Champa asks Chameli, “Don’t you think ABCD is a square?” Chameli disagrees.
Using distance formula, find which of them is correct.
If Q (0, 1) is equidistant from P (5, − 3) and R (x, 6), find the values of x. Also find the distance QR and PR.
Find a relation between x and y such that the point (x, y) is equidistant from the point (3, 6) and (−3, 4).
An equilateral triangle has two vertices at the points (3, 4) and (−2, 3), find the coordinates of the third vertex.
Show that the quadrilateral whose vertices are (2, −1), (3, 4) (−2, 3) and (−3,−2) is a rhombus.
The long and short hands of a clock are 6 cm and 4 cm long respectively. Find the sum of the distances travelled by their tips in 24 hours. (Use π = 3.14) ?
Find the distance between the following pair of point.
T(–3, 6), R(9, –10)
Determine whether the points are collinear.
P(–2, 3), Q(1, 2), R(4, 1)
Find the coordinate of O , the centre of a circle passing through A (8 , 12) , B (11 , 3), and C (0 , 14). Also , find its radius.
Calculate the distance between A (7, 3) and B on the x-axis, whose abscissa is 11.
Show that the points (a, a), (-a, -a) and `(-asqrt(3), asqrt(3))` are the vertices of an equilateral triangle.
The point which lies on the perpendicular bisector of the line segment joining the points A(–2, –5) and B(2, 5) is ______.
The distance between the point P(1, 4) and Q(4, 0) is ______.
∆ABC with vertices A(–2, 0), B(2, 0) and C(0, 2) is similar to ∆DEF with vertices D(–4, 0), E(4, 0) and F(0, 4).
Find a point which is equidistant from the points A(–5, 4) and B(–1, 6)? How many such points are there?
The points A(–1, –2), B(4, 3), C(2, 5) and D(–3, 0) in that order form a rectangle.
If the point A(2, – 4) is equidistant from P(3, 8) and Q(–10, y), find the values of y. Also find distance PQ.
A point (x, y) is at a distance of 5 units from the origin. How many such points lie in the third quadrant?
