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.
Advertisements
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 that:
sec2θ + cosec2θ = sec2θ x cosec2θ
(1 + tan θ + sec θ) (1 + cot θ − cosec θ) = ______.
Prove the following identities, where the angles involved are acute angles for which the expressions are defined:
`(sin theta-2sin^3theta)/(2cos^3theta -costheta) = tan theta`
Prove the following trigonometric identities.
tan2 θ − sin2 θ = tan2 θ sin2 θ
Prove the following trigonometric identities.
sin2 A cos2 B − cos2 A sin2 B = sin2 A − sin2 B
Prove the following identities:
`1/(1 + cosA) + 1/(1 - cosA) = 2cosec^2A`
Prove the following identities:
`(1 + cosA)/(1 - cosA) = tan^2A/(secA - 1)^2`
Prove the following identities:
`((cosecA - cotA)^2 + 1)/(secA(cosecA - cotA)) = 2cotA`
If sec A + tan A = p, show that:
`sin A = (p^2 - 1)/(p^2 + 1)`
`(sec^2 theta -1)(cosec^2 theta - 1)=1`
`(cot ^theta)/((cosec theta+1)) + ((cosec theta + 1))/cot theta = 2 sec theta`
`(sin theta)/((sec theta + tan theta -1)) + cos theta/((cosec theta + cot theta -1))=1`
`(cot^2 theta ( sec theta - 1))/((1+ sin theta))+ (sec^2 theta(sin theta-1))/((1+ sec theta))=0`
If `sin theta = x , " write the value of cot "theta .`
If cos A + cos2 A = 1, then sin2 A + sin4 A =
Prove the following identity :
`sqrt((1 - cosA)/(1 + cosA)) = sinA/(1 + cosA)`
Prove the following identity :
`tan^2A - tan^2B = (sin^2A - sin^2B)/(cos^2Acos^2B)`
If sinA + cosA = `sqrt(2)` , prove that sinAcosA = `1/2`
Prove that ( 1 + tan A)2 + (1 - tan A)2 = 2 sec2A
If tan θ = 3, then `(4 sin theta - cos theta)/(4 sin theta + cos theta)` is equal to ______.
