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y + 4x = 11 so y = -4x + 11 whose gradient is -4.

So gradient of line joining the two given points is 1/4.

Therefore (n - 2)/(6 - m) = 1/4

or 4*(n - 2) = 6 - m

that is 4n + m = 14

Also, the given line passes through the midpoint, [(m+6)/2, (2+n)/2]

so (2+n)/2 + 4*(m+6)/2 = 11

multiply through by 2 and simplify:

2 + n + 4m + 24 = 22

that is n + 4m = -4

Solving the two equations gives m = -2 and n = 4

4n + m = 14

-4(n + 4m = -4)

4n + m = 14

-4n - 16m = 16 add both equations

-15m = 30 divide by -15

m = -2

Substitute m with -2 into n + 4m = -4.

n - 8 = -4 add 8 to both sides

n = 4

Answer:

If the slope or gradient is 1/4 then m = -2 and n = 4 because (2-4)/(-2-6) = 1/4

The lines coordinates are (-2, 2) and (6, 4) and its equation is 4y = x + 10

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Q: What are the values of m and n given that y plus 4x equals 11 is the perpendicular bisector of the line joining m 2 to 6 n?
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