Advertisements
Advertisements
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.
Advertisements
उत्तर
Using distance formula, we have
AB = `sqrt((2-5)^2+(-2-2)^2)=sqrt(9+16)=5`
BC = `sqrt((-2-2)^2+(t+2)^2)=sqrt(t^2+4t+20)`
AC = `sqrt((-2-5)^2+(t-2)^2)=sqrt(t^2-4t+53) `
Now, it is given that △ABC is right angled at B.
Using the Pythagorean theorem, we have
AB2 + BC2 = AC2
∴25+t2+4t+20=t2−4t+53 [From (1), (2) and (3)]
⇒45+4t=−4t+53
⇒8t=8
⇒t=1
Hence, the value of t is 1.
APPEARS IN
संबंधित प्रश्न
Show that the quadrilateral whose vertices are (2, −1), (3, 4) (−2, 3) and (−3,−2) is a rhombus.
Using the distance formula, show that the given points are collinear:
(-2, 5), (0,1) and (2, -3)
Find the distance of the following point from the origin :
(5 , 12)
Find the distance of a point (13 , -9) from another point on the line y = 0 whose abscissa is 1.
Show that the points P (0, 5), Q (5, 10) and R (6, 3) are the vertices of an isosceles triangle.
KM is a straight line of 13 units If K has the coordinate (2, 5) and M has the coordinates (x, – 7) find the possible value of x.
The distance between point P(2, 2) and Q(5, x) is 5 cm, then the value of x ______
Show that the point (0, 9) is equidistant from the points (– 4, 1) and (4, 1)
The point which divides the lines segment joining the points (7, -6) and (3, 4) in ratio 1 : 2 internally lies in the ______.
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 ______.
