Advertisements
Advertisements
प्रश्न
Verify that the points A(–2, 2), B(2, 2) and C(2, 7) are the vertices of a right-angled triangle.
उत्तर
In a right angles triangle ABC, right-angled at B, according to the Pythagoras theorem
AB2 + BC2 = AC2
According to the distance formula, the distance 'd' between two points (a,b) and (c,d) is given by
`d = root(2)((a - c)^2 + (b - d)^2`....(1)
For the given points Distance between P and Q is
PQ = `sqrt((-2-2)^2 + (2 - 2)^2) = sqrt(16)`
QR = `sqrt((2-2)^2 + (7 - 2)^2) = sqrt(25)`
PR = `sqrt((-2-2)^2 + (2 - 7)^2) = sqrt(16 + 25) = sqrt(41)`
PQ2 = 16
QR2 = 25
PR2 = 41
As PQ2 + QR2 = PR2
Hence the given points form a right-angled triangle.
APPEARS IN
संबंधित प्रश्न
Prove the following trigonometric identities.
`cosec theta sqrt(1 - cos^2 theta) = 1`
Prove the following trigonometric identities.
`(1 + sin theta)/cos theta + cos theta/(1 + sin theta) = 2 sec theta`
Prove the following trigonometric identities.
`tan theta/(1 - cot theta) + cot theta/(1 - tan theta) = 1 + tan theta + cot theta`
Prove the following trigonometric identities.
(sec A − cosec A) (1 + tan A + cot A) = tan A sec A − cot A cosec A
Prove the following identities:
`(cosecA)/(cosecA - 1) + (cosecA)/(cosecA + 1) = 2sec^2A`
Prove the following identities:
`sqrt((1 + sinA)/(1 - sinA)) = sec A + tan A`
Show that none of the following is an identity:
(i) `cos^2theta + cos theta =1`
`If sin theta = cos( theta - 45° ),where theta " is acute, find the value of "theta` .
Simplify : 2 sin30 + 3 tan45.
If sec θ + tan θ = x, then sec θ =
If a cos θ + b sin θ = m and a sin θ − b cos θ = n, then a2 + b2 =
Prove the following identity :
`((1 + tan^2A)cotA)/(cosec^2A) = tanA`
Prove the following identity :
`(sinA - sinB)/(cosA + cosB) + (cosA - cosB)/(sinA + sinB) = 0`
Prove the following identity :
`2(sin^6θ + cos^6θ) - 3(sin^4θ + cos^4θ) + 1 = 0`
For ΔABC , prove that :
`sin((A + B)/2) = cos"C/2`
Without using trigonometric identity , show that :
`cos^2 25^circ + cos^2 65^circ = 1`
Prove the following identities.
`sqrt((1 + sin theta)/(1 - sin theta)) + sqrt((1 - sin theta)/(1 + sin theta))` = 2 sec θ
If `(cos alpha)/(cos beta)` = m and `(cos alpha)/(sin beta)` = n, then prove that (m2 + n2) cos2 β = n2
Choose the correct alternative:
`(1 + cot^2"A")/(1 + tan^2"A")` = ?
To prove cot θ + tan θ = cosec θ × sec θ, complete the activity given below.
Activity:
L.H.S = `square`
= `square/sintheta + sintheta/costheta`
= `(cos^2theta + sin^2theta)/square`
= `1/(sintheta*costheta)` ......`[cos^2theta + sin^2theta = square]`
= `1/sintheta xx 1/square`
= `square`
= R.H.S
