# maths

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The perpendicular bisector of the line joining the points D(1,2) and E(5,4) meets the y-axis at the point (0,k).calculate k

• maths -

First, find the midpoint of DE: ((1+5)/2,(2+4)/2) = (3,3)

Now, find the slope of the line DE: (4-2)/(5-1) = 2/4 = 1/2

You want a perpendicular line, so its slope will be -2

The equation of the desired line, using point-slope form:

(y-3)/(x-3) = -2
y-3 = -2x + 6
y = -2x + 9

The y-intercept is (0,9) so k=9

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