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The perpendicular bisector of the line segment joining p(1,4)and q(k, 3)has a y intercept 4 then k is equal to

The perpendicular bisector of the line segment joining p(1,4)and q(k, 3)has a y intercept 4 then k is equal to

Grade:11

1 Answers

Arun
25750 Points
6 years ago
 

Let the equation of perpendicular bisector is y = mx + c

c = -4

So, y = mx - 4 .............(i)

 



Center point between P(1, 4) and Q(k, 3) will be ((1+k)/2, 7/2)

In equation (i) passes thru ((1+k)/2, 7/2)

So, 7/2 = m((1+k)/2) - 4

7 = m + mk - 8

m + mk - 15 = 0 .................(ii)

 



m = gradient of the perpendiculat line

m = - (gradient of PQ) = -(1-k)/(4-3) = k - 1
 

 

Replace value of m in equation (ii)

k - 1 + k(k - 1) - 15 = 0

k2 = 16

k = ±4

 

Let the equation of perpendicular bisector is y = mx + c

c = -4

So, y = mx - 4 .............(i)

 



Center point between P(1, 4) and Q(k, 3) will be ((1+k)/2, 7/2)

In equation (i) passes thru ((1+k)/2, 7/2)

So, 7/2 = m((1+k)/2) - 4

7 = m + mk - 8

m + mk - 15 = 0 .................(ii)

 



m = gradient of the perpendiculat line

m = - (gradient of PQ) = -(1-k)/(4-3) = k - 1
 

 

Replace value of m in equation (ii)

k - 1 + k(k - 1) - 15 = 0

k2 = 16

k = ±4

 

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