Advertisements
Advertisements
Question
Find distance CD where C(– 3a, a), D(a, – 2a)
Advertisements
Solution
Let C(x1, y1) and D(x2, y2) be the given points
∴ x1 = – 3a, y1 = a, x2 = a, y2 = – 2a
By distance formula,
d(C, D) = `sqrt((x_2 - x_1)^2 + (y_2 - y_1)^2`
= `sqrt(["a" - (-3"a")]^2 + (-2"a" - "a")^2`
= `sqrt(("a" + 3"a")^2 + (-2"a" - "a")^2`
= `sqrt((4"a")^2 + (-3"a")^2`
= `sqrt(16"a"^2 + 9"a"^2)`
= `sqrt(25"a"^2)`
∴ d(C, D) = 5a units
RELATED QUESTIONS
Show that the points (a, a), (–a, –a) and (– √3 a, √3 a) are the vertices of an equilateral triangle. Also find its area.
If the opposite vertices of a square are (1, – 1) and (3, 4), find the coordinates of the remaining angular points.
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.
Show that the ▢PQRS formed by P(2, 1), Q(–1, 3), R(–5, –3) and S(–2, –5) is a rectangle.
Find the distance of the following point from the origin :
(6 , 8)
Find the distance between the following point :
(p+q,p-q) and (p-q, p-q)
Find the distance between the following pairs of points:
`(3/5,2) and (-(1)/(5),1(2)/(5))`
What point on the x-axis is equidistant from the points (7, 6) and (-3, 4)?
A point P lies on the x-axis and another point Q lies on the y-axis.
Write the abscissa of point Q.
Point P (2, -7) is the center of a circle with radius 13 unit, PT is perpendicular to chord AB and T = (-2, -4); calculate the length of: AT
Seg OA is the radius of a circle with centre O. The coordinates of point A is (0, 2) then decide whether the point B(1, 2) is on the circle?
The distance between the points A(0, 6) and B(0, -2) is ______.
The coordinates of the point which is equidistant from the three vertices of the ΔAOB as shown in the figure is ______.
The distance of the point P(–6, 8) from the origin is ______.
The points (– 4, 0), (4, 0), (0, 3) are the vertices of a ______.
Points A(4, 3), B(6, 4), C(5, –6) and D(–3, 5) are the vertices of a parallelogram.
Find a point which is equidistant from the points A(–5, 4) and B(–1, 6)? How many such points are there?
Show that points A(–1, –1), B(0, 1), C(1, 3) are collinear.
The distance of the point (5, 0) from the origin is ______.
A point (x, y) is at a distance of 5 units from the origin. How many such points lie in the third quadrant?
