Question

If the straight lines y=4-3x,ay=x+10,2y + bx+9=0 respect the three consecutive sides of a rectangles then ab=

Answer 1

Answer:

heyyy

For y = -3x + 4, the slope is -3, so 2y + bx + 9 = 0 must also have a slope of -3:

2y = -bx - 9

y = (-bx - 9) / 2

y = (-b/2)x - 4.5  

-b/2 = -3

b/2 = 3

b = 3 * 2

b = 6

So ay = x + 10 must be perpendicular to the lines above, so its slope must be the negative reciprocal of -3, which is 1/3:

y = (x + 10) / a

y = (1/a)x + (10/a)

1/a = 1/3

a = 3

ab = 3*6 = 18

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