Advertisements
Advertisements
प्रश्न
Find the value of a, if the distance between the points A(–3, –14) and B(a, –5) is 9 units.
Advertisements
उत्तर
Distance between two points (x1, y1) ( x2, y2) is:
d = `sqrt((x_2 - x_1)^2 + (y_2 - y_1)^2`
Distance between A(–3, –14) and B(a, –5) is:
d = `sqrt([(a + 3)^2 + (-5 + 14)^2])` = 9
Squaring on L.H.S and R.H.S.
(a + 3)2 + 81 = 81
(a + 3)2 = 0
(a + 3)(a + 3) = 0
a + 3 = 0
a = –3
APPEARS IN
संबंधित प्रश्न
If P (2, – 1), Q(3, 4), R(–2, 3) and S(–3, –2) be four points in a plane, show that PQRS is a rhombus but not a square. Find the area of the rhombus
Name the type of quadrilateral formed, if any, by the following point, and give reasons for your answer:
(−3, 5), (3, 1), (0, 3), (−1, −4)
Name the type of quadrilateral formed, if any, by the following point, and give reasons for your answer:
(4, 5), (7, 6), (4, 3), (1, 2)
Show that the points A (1, −2), B (3, 6), C (5, 10) and D (3, 2) are the vertices of a parallelogram.
Find the circumcenter of the triangle whose vertices are (-2, -3), (-1, 0), (7, -6).
Two opposite vertices of a square are (-1, 2) and (3, 2). Find the coordinates of other two
vertices.
Using the distance formula, show that the given points are collinear:
(1, -1), (5, 2) and (9, 5)
Find the distance between the following pairs of point in the coordinate plane :
(4 , 1) and (-4 , 5)
Find the relation between x and y if the point M (x,y) is equidistant from R (0,9) and T (14 , 11).
Given A = (x + 2, -2) and B (11, 6). Find x if AB = 17.
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.
Use distance formula to show that the points A(-1, 2), B(2, 5) and C(-5, -2) are collinear.
Find distance of point A(6, 8) from origin
Show that the point (0, 9) is equidistant from the points (– 4, 1) and (4, 1)
AOBC is a rectangle whose three vertices are A(0, 3), O(0, 0) and B(5, 0). The length of its diagonal is ______.
The distance between the point P(1, 4) and Q(4, 0) 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:
What are the coordinates of the position of a player Q such that his distance from K is twice his distance from E and K, Q and E are collinear?
If (– 4, 3) and (4, 3) are two vertices of an equilateral triangle, find the coordinates of the third vertex, given that the origin lies in the interior of the triangle.
The points A(–1, –2), B(4, 3), C(2, 5) and D(–3, 0) in that order form a rectangle.
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.
