ಮಾದರಿ ನಿರ್ದೇಶಾಂಕ ರೇಖಾಗಣಿತ

ನಿರ್ದೇಶಾಂಕ ರೇಖಾಗಣಿತ

ಮಾದರಿ ಪ್ರಶ್ನೆಗಳು

ಉತ್ತರ:
P(x, y) = P(3, 4)
x = 3,
y = 4

P(x, y) = √ (x2+ y2) 

P(3,4) = √ (32+ 42) 

          = √ (9+ 16) 

          = √ 25 

          = 5

ಉತ್ತರ:
P(x, y) = P(-6, -8)
x = -6
y = -8

P(x, y)    = √ (x2+ y2) 

P(-6,-8) = √ (-6)2+ (-8)2 

             = √ (36+ 64) 

             = √ 100 

             = 10

ಉತ್ತರ:
P(x, y) = P(-8, 15)
x = 8
y = 15

P(x, y)    = √ (x2+ y2) 

P(-8,15) = √ (-8)2+ 152 

             = √ (64+ 225) 

             = √ 289 

             = 17

ಉತ್ತರ:
(x1,y1) = (-5, 7)
(x2,y2) = (-1, 3)

AB = √ (x₂ - x₁)2+ (y₂ - y₁)2 

AB = √ (-1)-(-5)2+ (3-7)2 

AB = √ (-1)+52+ (-4)2 

AB = √ 42+ (-4)2 

AB = √ 16+ 16 

AB = √ 32 

AB = 2√ 2 

ಉತ್ತರ:
(x1,y1) = (2, 3)
(x2,y2) = (6, 6)

PQ = √ (x₂ - x₁)2+ (y₂ - y₁)2 

PQ = √ (6-2)2+ (6-3)2 

PQ = √ 42+ 32 

PQ = √ 16+ 9 

PQ = √ 25 

PQ = 5

ಉತ್ತರ:
(x1,y1) = (2, -2)
(x2,y2) = (14, 10)

PQ = √ (x₂ - x₁)2+ (y₂ - y₁)2 

PQ = √ (14-2)2+ ((10-(-2))2 

PQ = √ 122+ (10+2)2 

PQ = √ 144+ 122 

PQ = √ 144+ 144  

PQ = √ 288 

PQ = 12√ 2 

ಉತ್ತರ:
(x1,y1) = (2, 4)
(x2,y2) = (3, 10)

P(x,y) = (
(x2+x1) / 2
,
(y2+y1) / 2
)

           = (
(2+3) / 2
,
(4+10) / 2
)

           = (
5 / 2
,
14 / 2
)

           = (
5 / 2
, 7 )

ಉತ್ತರ:
(x1,y1) = (-3, 2)
(x2,y2) = (-1, -4)

P(x,y) = (
(x2+x1) / 2
,
(y2+y1) / 2
)

           = (
(-1+(-3) / 2
,
-4+2 / 2
)

           = (
-4 / 2
,
-2 / 2
)

           = (-2, -1 )

ಉತ್ತರ:
(x1,y1) = (-3, 2)
(x2,y2) = (-1, -4)
m1:m2 = 3:1

P(x,y) = (
(m1x2+m2x1) / (m1+m2)
,
(m1y2+m2y1) / (m1+m2)
)

P(x,y) = (
3(8)+1(4) / 3+1
,
3(5)+1(-3) / 3+1
)

P(x,y) = (
24+4 / 4
,
15-3 / 4
)

P(x,y) = (
28 / 4
,
12 / 4
)

P(x,y) = (7, 3)

ಉತ್ತರ:
(x1,y1) = (-1, 7)
(x2,y2) = (4, -3)
m1:m2 = 2:3

P(x,y) = (
(m1x2+m2x1) / (m1+m2)
,
(m1y2+m2y1) / (m1+m2)
)

P(x,y) = (
2(4)+3(-1) / 2+3
,
2(-3)+3(7) / 2+3
)

P(x,y) = (
8-3 / 5
,
-6+21 / 5
)

P(x,y) = (
5 / 5
,
15 / 5
)

P(x,y) = (1, 3)

ಉತ್ತರ:
(x1,y1) = (1, -1)
(x2,y2) = (-4, 6)
(x3,y3) = (-3, -5)

ತ್ರಿಭುಜದ ವಿಸ್ತೀರ್ಣ:

A =
1 / 2
 [x₁(y₂ - y₃) + x₂(y₃ - y₁) + x₃(y₁ - y₂)]

A =
1 / 2
 [1(6-(-5))+(-4)(-5-(-1))+(-3)(-1-6)]

A =
1 / 2
 [1(6+5)+(-4)(-5+1)+(-3)(-7)]

A =
1 / 2
 [1(11)+(-4)(-4)+21]

A =
1 / 2
 [11+16+21]

A =
1 / 2
 [48]

A = 24

ಉತ್ತರ:
(x1,y1) = (2, 3)
(x2,y2) = (-1, 0)
(x3,y3) = (2, -4)

ತ್ರಿಭುಜದ ವಿಸ್ತೀರ್ಣ:

A =
1 / 2
 [x₁(y₂ - y₃) + x₂(y₃ - y₁) + x₃(y₁ - y₂)]

A =
1 / 2
 [2(0-(-4))+(-1)(-4-3)+2(3-0)]

A =
1 / 2
 [2(0+4)+(-1)(-7)+2(3)]

A =
1 / 2
 [2(4)+7+6]

A =
1 / 2
 [8+7+6]

A =
1 / 2
 [21]

A = 10.5