Question

Find an equation of the line that satisfies the given conditions. Through (5, 7); perpendicular to the line y = 4

Find an equation of the line that satisfies the given conditions. Through (−5, −7); perpendicular to the line passing through (−2, 5) and (2, 3)

Answer 1

solution

(1) the equation of the line perpendicular to y=4 we can write as 0x+y-4=0

now the equation of any straight line perpendicular to 0x+y-4 =0 is of the form

x-0y+k=0 ...(1) interchange coeffient of x and y

the point (5,7) lies on the line

x-0y+k=0

5-0+k=0

k=-5 substitute in (1)

the equation of the required line is x-5=0

(or)x=5

(2) let the given points be A(-2,5) B(2,3)

slope of AB m₁ =y₂-y₁ /x₂-x₁

   3-5/2-(-2)

=-2/4

=-1/2

let m₂ be the slope of the required line since the required line is perpendicular to AB

therefore m_1*  m₂ =-1

-1/2*m₂ =-1

m₂ =-1*-2/1

m_{2 =2}

the required line passes through the point(-5,-7)

the equation of required line

y-y1=m2(x-x1)

y-(-7)=2(x-(-5)

y+7 =2(x+5)

y+7=2x +10

2x-y+3 =0 this is the required equation