Advertisements
Advertisements
Question
Show that the point (11, –2) is equidistant from (4, –3) and (6, 3).
Advertisements
Solution
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
RELATED QUESTIONS
Find the distance between the points (0, 0) and (36, 15). Can you now find the distance between the two towns A and B discussed in Section 7.2.
The length of a line segment is of 10 units and the coordinates of one end-point are (2, –3). If the abscissa of the other end is 10, find the ordinate of the other end.
Find the distance between the points:
A(1, –3) and B(4, –6)
Find the distance between the points `A((-8)/5, 2)` and `B(2/5, 2)`.
For what values of k are the points (8, 1), (3, –2k) and (k, –5) collinear ?
Find the distance between the following pair of point.
P(–5, 7), Q(–1, 3)
Find the distance between the following pair of points.
L(5, –8), M(–7, –3)
Find the distance between the following pair of point.
T(–3, 6), R(9, –10)
Find the distance between the following point :
(sec θ , tan θ) and (- tan θ , sec θ)
P(5 , -8) , Q (2 , -9) and R(2 , 1) are the vertices of a triangle. Find tyhe circumcentre and the circumradius of the triangle.
Prove that the points (1 ,1),(-4 , 4) and (4 , 6) are the certices of an isosceles triangle.
A(2, 5), B(-2, 4) and C(-2, 6) are the vertices of a triangle ABC. Prove that ABC is an isosceles triangle.
What point on the x-axis is equidistant from the points (7, 6) and (-3, 4)?
Prove that the points A (1, -3), B (-3, 0) and C (4, 1) are the vertices of an isosceles right-angled triangle. Find the area of the triangle.
Find the distance of the following points from origin.
(a+b, a-b)
Points A(4, 3), B(6, 4), C(5, –6) and D(–3, 5) are the vertices of a parallelogram.
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.
If (a, b) is the mid-point of the line segment joining the points A(10, –6) and B(k, 4) and a – 2b = 18, find the value of k and the distance AB.
Find the distance between the points O(0, 0) and P(3, 4).
