Advertisements
Advertisements
Question
If x is a positive integer such that the distance between points P (x, 2) and Q (3, −6) is 10 units, then x =
Options
3
-3
9
-9
Advertisements
Solution
It is given that distance between P (x, 2) and Q(3 , - 6 ) is 10.
In general, the distance between A(x1 , y 1 ) and B (x2 , y2) is given by,
`AB^2 = ( x_2-x_1)^2 + (y_2 - y_1)^2`
So,
`10^2 = (x - 3)^2 + (2 + 6)^2`
On further simplification,
`(x - 3)^2 = 36 `
` x = 3 +- 6`
`= 9 - 3`
We will neglect the negative value. So,
x = 9
APPEARS IN
RELATED QUESTIONS
A line intersects the y-axis and x-axis at the points P and Q respectively. If (2, –5) is the mid-point of PQ, then find the coordinates of P and Q.
On which axis do the following points lie?
S(0,5)
Find the third vertex of a triangle, if two of its vertices are at (−3, 1) and (0, −2) and the centroid is at the origin.
Find the point on x-axis which is equidistant from the points (−2, 5) and (2,−3).
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.
Show that the points A (1, 0), B (5, 3), C (2, 7) and D (−2, 4) are the vertices of a parallelogram.
The line joining the points (2, 1) and (5, −8) is trisected at the points P and Q. If point P lies on the line 2x − y + k = 0. Find the value of k.
If the point C ( - 2,3) is equidistant form the points A (3, -1) and Bx (x ,8) , find the value of x. Also, find the distance between BC
Show that the points A(6,1), B(8,2), C(9,4) and D(7,3) are the vertices of a rhombus. Find its area.
Show hat A(1,2), B(4,3),C(6,6) and D(3,5) are the vertices of a parallelogram. Show that ABCD is not rectangle.
Find the area of the triangle formed by joining the midpoints of the sides of the triangle whose vertices are A(2,1) B(4,3) and C(2,5)
Find the coordinates of the centre of the circle passing through the points P(6, –6), Q(3, –7) and R (3, 3).
Show that A(-4, -7), B(-1, 2), C(8, 5) and D(5, -4) are the vertices of a
rhombus ABCD.
The perpendicular distance of the point P (4, 3) from x-axis is
Find the value of k, if the points A(7, −2), B (5, 1) and C (3, 2k) are collinear.
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 points (t, 2t), (−2, 6) and (3, 1) are collinear, then t =
Find the coordinates of point A, where AB is a diameter of the circle with centre (–2, 2) and B is the point with coordinates (3, 4).
Find the coordinates of the point of intersection of the graph of the equation x = 2 and y = –3.
If the coordinate of point A on the number line is –1 and that of point B is 6, then find d(A, B).
