Advertisements
Advertisements
प्रश्न
Name the type of triangle formed by the points A(–5, 6), B(–4, –2) and C(7, 5).
Advertisements
उत्तर
To find the type of triangle, first we determine the length of all three sides and see whatever condition of triangle is satisfy by these sides.
Now, using distance formula between two points,
AB = `sqrt((-4 + 5)^2 + (-2 - 6)^2` ...`[∵ d = sqrt((x_2 - x_1)^2 + (y_2 - y_1)^2)]`
= `sqrt((1)^2 + (-8)^2`
= `sqrt(1 + 64)`
= `sqrt(65)`
BC = `sqrt((7 + 4)^2 + (5 + 2)^2`
= `sqrt((11)^2 + (7)^2`
= `sqrt(121 + 49)`
= `sqrt(170)`
And CA = `sqrt((-5 - 7)^2 + (6 - 5)^2`
= `sqrt((-12)^2 + (1)^2`
= `sqrt(144 + 1)`
= `sqrt(145)`
We see that,
AB ≠ BC ≠ CA
And not hold the condition of Pythagoras in a ΔABC.
i.e., (Hypotenuse)2 = (Base)2 + (Perpendicular)2
Hence, the required triangle is scalene because all of its sides are not equal i.e., different to each other.
APPEARS IN
संबंधित प्रश्न
If A(5, 2), B(2, −2) and C(−2, t) are the vertices of a right angled triangle with ∠B = 90°, then find the value of t.
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 points, and give reasons for your answer:
(- 1, - 2), (1, 0), (- 1, 2), (- 3, 0)
An equilateral triangle has two vertices at the points (3, 4) and (−2, 3), find the coordinates of the third vertex.
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.
`" Find the distance between the points" A ((-8)/5,2) and B (2/5,2)`
Find the distance between the following pair of point in the coordinate plane.
(1 , 3) and (3 , 9)
Find the distance between the following pairs of point in the coordinate plane :
(7 , -7) and (2 , 5)
The centre of a circle passing through P(8, 5) is (x+l , x-4). Find the coordinates of the centre if the diameter of the circle is 20 units.
Prove that the points (4 , 6) , (- 1 , 5) , (- 2, 0) and (3 , 1) are the vertices of a rhombus.
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.
Find the distance between the following pair of points:
`(sqrt(3)+1,1)` and `(0, sqrt(3))`
Find the point on y-axis whose distances from the points A (6, 7) and B (4, -3) are in the ratio 1: 2.
The distances of point P (x, y) from the points A (1, - 3) and B (- 2, 2) are in the ratio 2: 3.
Show that: 5x2 + 5y2 - 34x + 70y + 58 = 0.
Find distance between point A(7, 5) and B(2, 5).
Find distance between points O(0, 0) and B(–5, 12).
Show that the point (0, 9) is equidistant from the points (–4, 1) and (4, 1).
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 coordinates of the centroid of ΔEHJ are ______.
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?
The point A(2, 7) lies on the perpendicular bisector of line segment joining the points P(6, 5) and Q(0, – 4).
