Question

6x-3y+27=0 और 2x-y+9=0

Q5. X और Y में संबंध ज्ञात करें यदि X, Y (1, 2)और (7, 0) समदूरस्थ है।​

Answer 1

Answer:

Step-by-step explanation:

We are going to use follow formulas and information.

- Coordinates of midpoint of two endpoints A( $x_{1}$ , $y_{1}$ ) and B( $x_{2}$ , $y_{2}$ ) of a line segment are

( $\frac{x_{1} +x_{2} }{2}$ , $\frac{y_{1} +y_{2} }{2}$ )

- Slope "m" of a line passing through points A and B

m = $\frac{y_{2} - y_{1} }{x_{2} -x_{1} }$

- Slope - point equation of a line passing through the points A and B

y - $y_{1}$ = m( x - $x_{1}$ )

- Slope of two perpendicular lines $m_{1}$ and $m_{2}$ are opposite reciprocals

$m_{1}$ $m_{2}$ = - 1

- Perpendicular bisector is a line which cuts a line segment into two equal parts at 90° and every point in the perpendicular bisector is equidistant from point A and B.

~~~~~~~~~~~~~~~~~~~~~~~~~~~~

A(1, 2)

B(7, 0)

( $\frac{1+7}{2}$ , $\frac{2+0}{2}$ ) = ( 4, 1 )

$m_{AB}$ = $\frac{0-2}{7-1}$ = - $\frac{1}{3}$

Slope "m" of perpendicular line is 3 .

Equation of the perpendicular bisector ( the relation between "x" and "y" ) is

y - 1 = 3(x - 4) (slope-point form)

y = 3x - 11 (slope-intercept form)

3x - y - 11 = 0 (standard form)

Answer 2

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Compare the Equations with

6x-3y+27=0

2x-y+9=0

We get,

a1 = 6

a2 = 2

b1 = -3

b2 = -1

c1 = 10

c2 = 9

a1/a2

= 6/2

= 3

b1/b2

= -3/-1

= 3

c1/c2

= 10/9

a1/a2 = b1/b2 = c1/c2

So, the Equation has no Solution

Hence,the Lines are Parallel.

_________ X _________

Q5.यदि बिंदु (x,y),(1,2) और (7,0) संरेखी हैं। तो इसका मतलब यह है कि यह एक त्रिभुज का निर्माण नहीं कर सकते अर्थात इन तीनों बिंदुओं के द्वारा बनाए गए त्रिभुज का क्षेत्रफल 0 होगा |

तीन बिंदुओं से निर्मित त्रिभुज का क्षेत्रफल का सूत्र:

½(x¹ (y² - y³) + x²(y³-y¹) + x³(y¹ - y²)

½(x(2-0) + 1(0-y) + 7(y-2)) = 0

=> 2x - y + 7y - 14 = 0

=> 2x + 6y - 14 = 0

x + 3y - 7 = 0

x + 3y = 7

x और y का संबंध इस प्रकार इस समीकरण से बनेगा|