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The perpendicular bisector of the line segment joining P (1,4) and Q (k,3) has y intersept-4 then a possible value of k is
Dear studentLet the equation of perpendicular bisector is y = mx + cc = -4So, 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) - 47 = m + mk - 8m + mk - 15 = 0 .................(ii)m = gradient of the perpendiculat linem = - (gradient of PQ) = -(1-k)/(4-3) = k - 1Replace value of m in equation (ii)k - 1 + k(k - 1) - 15 = 0k2 = 16k = ±4 RegardsArun (askIITians forum expert)
Let the equation of perpendicular bisector is y = mx + cc = -4So, 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) - 47 = m + mk - 8m + mk - 15 = 0 .................(ii)
m = gradient of the perpendiculat linem = - (gradient of PQ) = -(1-k)/(4-3) = k - 1
Replace value of m in equation (ii)k - 1 + k(k - 1) - 15 = 0k2 = 16k = ±4
Regards
Arun (askIITians forum expert)
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