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 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
If Q (0, 1) is equidistant from P (5, − 3) and R (x, 6), find the values of x. Also find the distance QR and PR.
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.
If the point P(x, y ) is equidistant from the points A(5, 1) and B (1, 5), prove that x = y.
Find the distance between the points
A(1,-3) and B(4,-6)
Find the distance between the points:
P(a + b, a - b) and Q(a - b, a + b)
The long and short hands of a clock are 6 cm and 4 cm long respectively. Find the sum of the distances travelled by their tips in 24 hours. (Use π = 3.14) ?
Determine whether the points are collinear.
L(–2, 3), M(1, –3), N(5, 4)
Determine whether the points are collinear.
P(–2, 3), Q(1, 2), R(4, 1)
Find the distance between the following pair of point in the coordinate plane.
(1 , 3) and (3 , 9)
Find the distance of the following point from the origin :
(6 , 8)
x (1,2),Y (3, -4) and z (5,-6) are the vertices of a triangle . Find the circumcentre and the circumradius of the triangle.
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.
(a cos θ, a sin θ).
Use distance formula to show that the points A(-1, 2), B(2, 5) and C(-5, -2) are collinear.
The distance between point P(2, 2) and Q(5, x) is 5 cm, then the value of x ______
A circle drawn with origin as the centre passes through `(13/2, 0)`. The point which does not lie in the interior of the circle 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:
If a player P needs to be at equal distances from A and G, such that A, P and G are in straight line, then position of P will be given by ______.
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?
A point (x, y) is at a distance of 5 units from the origin. How many such points lie in the third quadrant?
