Advertisements
Advertisements
Question
If the distance between the points (4, P) and (1, 0) is 5, then the value of p is ______.
Options
4 only
± 4
– 4 only
0
Advertisements
Solution
If the distance between the points (4, p) and (1, 0) is 5, then the value of p is ± 4.
Explanation:
According to the question,
The distance between the points (4, p) and (1, 0) = 5
d = `sqrt((x_2 - x_1)^2 + (y_2 - y_1)^2`
i.e., `sqrt((1 - 4)^2 + (0 - "p")^2` = 5
⇒ `sqrt((-3)^2 + "p"^2)` = 5
⇒ `sqrt(9 + "p"^2)` = 5
On squaring both the sides, we get
9 + p2 = 25
⇒ p2 = 16
⇒ p = ± 4
Hence, the required value of p is ± 4.
APPEARS IN
RELATED QUESTIONS
Find the value of x, if the distance between the points (x, – 1) and (3, 2) is 5.
If the point P(x, y ) is equidistant from the points A(5, 1) and B (1, 5), prove that x = y.
Given a triangle ABC in which A = (4, −4), B = (0, 5) and C = (5, 10). A point P lies on BC such that BP : PC = 3 : 2. Find the length of line segment AP.
If P (x , y ) is equidistant from the points A (7,1) and B (3,5) find the relation between x and y
Find the distance between the following pairs of point.
W `((- 7)/2 , 4)`, X (11, 4)
Determine whether the points are collinear.
P(–2, 3), Q(1, 2), R(4, 1)
Find the distance of a point (12 , 5) from another point on the line x = 0 whose ordinate is 9.
Find the coordinates of O, the centre passing through A( -2, -3), B(-1, 0) and C(7, 6). Also, find its radius.
Prove that the points (4 , 6) , (- 1 , 5) , (- 2, 0) and (3 , 1) are the vertices of a rhombus.
ABC is an equilateral triangle . If the coordinates of A and B are (1 , 1) and (- 1 , -1) , find the coordinates of C.
Find the distance between the points (a, b) and (−a, −b).
Show that the points P (0, 5), Q (5, 10) and R (6, 3) are the vertices of an isosceles triangle.
Find distance between point Q(3, – 7) and point R(3, 3)
Solution: Suppose Q(x1, y1) and point R(x2, y2)
x1 = 3, y1 = – 7 and x2 = 3, y2 = 3
Using distance formula,
d(Q, R) = `sqrt(square)`
∴ d(Q, R) = `sqrt(square - 100)`
∴ d(Q, R) = `sqrt(square)`
∴ d(Q, R) = `square`
Show that the points (2, 0), (– 2, 0) and (0, 2) are vertices of a triangle. State the type of triangle with reason
Using distance formula decide whether the points (4, 3), (5, 1), and (1, 9) are collinear or not.
The point which divides the lines segment joining the points (7, -6) and (3, 4) in ratio 1 : 2 internally lies in the ______.
Point P(0, 2) is the point of intersection of y-axis and perpendicular bisector of line segment joining the points A(–1, 1) and B(3, 3).
|
Case Study Trigonometry in the form of triangulation forms the basis of navigation, whether it is by land, sea or air. GPS a radio navigation system helps to locate our position on earth with the help of satellites. |
- Make a labelled figure on the basis of the given information and calculate the distance of the boat from the foot of the observation tower.
- After 10 minutes, the guard observed that the boat was approaching the tower and its distance from tower is reduced by 240(`sqrt(3)` - 1) m. He immediately raised the alarm. What was the new angle of depression of the boat from the top of the observation tower?
Find distance between points P(– 5, – 7) and Q(0, 3).
By distance formula,
PQ = `sqrt(square + (y_2 - y_1)^2`
= `sqrt(square + square)`
= `sqrt(square + square)`
= `sqrt(square + square)`
= `sqrt(125)`
= `5sqrt(5)`
Find the distance between the points O(0, 0) and P(3, 4).
