Question

for what value of k, the line joining 3x-ky+7=0 is perpendicular to the line joining (4 ,3) and ( 5, -3).

Answer 1

• k = 18

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Given

Line 1

• 3x - ky + 7 = 0

Line 2

• Passing through the points (4, 3) and (5, - 3)

To find

• The value of k, if the lines are perpendicular

Solution

We know the perpendicular lines have opposite reciprocal slopes, that is the product of their slopes is - 1.

Find the slope of line 1 by converting the equation into slope-intercept from standard form:

Info:

• standard form is ⇒ ax + by + c = 0,
• slope - intercept form is ⇒ y = mx + b, where m is the slope

• 3x - ky + 7 = 0
• ky = 3x + 7
• y = (3/k)x + 7/k

Its slope is 3/k.

Find the slope of line 2, using the slope formula:

• m = (y₂ - y₁)/(x₂ - x₁) = (-3 - 3)/(5 - 4) = - 6/1 = - 6

We have both the slopes now. Find their product:

• (3/k)*(- 6) = - 1
• - 18/k = - 1
• k = 18

So when k is 18, the lines are perpendicular.