Advertisements
Advertisements
Question
If the length of the segment joining point L(x, 7) and point M(1, 15) is 10 cm, then the value of x is ______
Options
7
7 or – 5
–1
1
Advertisements
Solution
7 or – 5
Here, x1 = x, y1 = 7, x2 = 1, y2 = 15
By distance formula,
d(L, M) = `sqrt((x_2 - x_1)^2 + (y_2 - y_1)^2)`
∴ d(L, M) = `sqrt((1 - x)^2 + (15 - 7)^2)`
∴ 10 = `sqrt((1 - x)^2 + 8^2)`
∴ 100 = (1 - x)2 + 64 ...[Squaring both sides]
∴ (1 - x)2 = 100 - 64
∴ (1 - x)2 = 36
∴ 1 - x = `+-sqrt(36)` ...[Taking square root of both sides]
∴ 1 - x = `+-6`
∴ 1 - x = 6 or 1 - x = -6
∴ x = -5 or x = 7
∴ The value of x is -5 or 7.
RELATED QUESTIONS
If the point (x, y) is equidistant from the points (a + b, b – a) and (a – b, a + b), prove that bx = ay.
Given a line segment AB joining the points A(–4, 6) and B(8, –3). Find
1) The ratio in which AB is divided by y-axis.
2) Find the coordinates of the point of intersection.
3) The length of AB.
Find the distance between the points
P(a sin ∝,a cos ∝ )and Q( acos ∝ ,- asin ∝)
Using the distance formula, show that the given points are collinear:
(-1, -1), (2, 3) and (8, 11)
Determine whether the points are collinear.
P(–2, 3), Q(1, 2), R(4, 1)
Show that the points A(1, 2), B(1, 6), C(1 + 2`sqrt3`, 4) are vertices of an equilateral triangle.
Find the distance between the following point :
(p+q,p-q) and (p-q, p-q)
Find the relation between x and y if the point M (x,y) is equidistant from R (0,9) and T (14 , 11).
Prove that the points (6 , -1) , (5 , 8) and (1 , 3) are the vertices of an isosceles triangle.
PQR is an isosceles triangle . If two of its vertices are P (2 , 0) and Q (2 , 5) , find the coordinates of R if the length of each of the two equal sides is 3.
In what ratio does the point P(−4, y) divides the line segment joining the points A(−6, 10) and B(3, −8)? Hence find the value of y.
The distance between the points (3, 1) and (0, x) is 5. Find x.
Point P (2, -7) is the centre of a circle with radius 13 unit, PT is perpendicular to chord AB and T = (-2, -4); calculate the length of AB.
The points A (3, 0), B (a, -2) and C (4, -1) are the vertices of triangle ABC right angled at vertex A. Find the value of a.
Find the distance of the following points from origin.
(5, 6)
The equation of the perpendicular bisector of line segment joining points A(4,5) and B(-2,3) is ______.
Case Study -2
A hockey field is the playing surface for the game of hockey. Historically, the game was played on natural turf (grass) but nowadays it is predominantly played on an artificial turf.
It is rectangular in shape - 100 yards by 60 yards. Goals consist of two upright posts placed equidistant from the centre of the backline, joined at the top by a horizontal crossbar. The inner edges of the posts must be 3.66 metres (4 yards) apart, and the lower edge of the crossbar must be 2.14 metres (7 feet) above the ground.
Each team plays with 11 players on the field during the game including the goalie. Positions you might play include -
- Forward: As shown by players A, B, C and D.
- Midfielders: As shown by players E, F and G.
- Fullbacks: As shown by players H, I and J.
- Goalie: As shown by player K.
Using the picture of a hockey field below, answer the questions that follow:
The point on x axis equidistant from I and E is ______.
|
In a GPS, The lines that run east-west are known as lines of latitude, and the lines running north-south are known as lines of longitude. The latitude and the longitude of a place are its coordinates and the distance formula is used to find the distance between two places. The distance between two parallel lines is approximately 150 km. A family from Uttar Pradesh planned a round trip from Lucknow (L) to Puri (P) via Bhuj (B) and Nashik (N) as shown in the given figure below.
|
Based on the above information answer the following questions using the coordinate geometry.
- Find the distance between Lucknow (L) to Bhuj (B).
- If Kota (K), internally divide the line segment joining Lucknow (L) to Bhuj (B) into 3 : 2 then find the coordinate of Kota (K).
- Name the type of triangle formed by the places Lucknow (L), Nashik (N) and Puri (P)
[OR]
Find a place (point) on the longitude (y-axis) which is equidistant from the points Lucknow (L) and Puri (P).
Find the distance between the points O(0, 0) and P(3, 4).
Show that points A(–1, –1), B(0, 1), C(1, 3) are collinear.
