The line AB is shown on the grid. b)Find the equation of the line
perpendicular to AB and passing
through the midpoint of AB.

Step-by-step explanation:

a)

first step: find the gradient slope of line AB

A(-1,-2) B(7,2)

gradient=change in y/change in x

M=[2-(-2)]/[7-(-1)

M=4/8

M=1/2

the gradient of the straight line is given by

M1*M2=-1

1/2*M2=-1

multiply both sides by the reciprocal of 1/2

2*1/2*M2=-1*2

M2= -2.

b)

first find the mind point of line AB

A(-1,-2) B(7,2)

M.P=(x1+x2)/2 ,(y+y2)/2

M.P=(-1+7)/2 ,(-2+2)/2

M.P=6/2 ,0/2

M.P=3,0

ALSO THE GRADIENT PERPENDICULAR TO LINE AB IS;

M= -2

equation of a line perpendicular to AB and passes through the midpoint of AB

Y-Y1=M(X-X1). (3,0). M=-2

y-0=-2(x-3)

y= -2x+6

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step-by-step explanation:

d. $180

step-by-step explanation:

if the dimensions of the room is 9ft by 12 ft, we have the area of the floor as,

so the area of the floor is 108 square feet, converting that into square yards we get,

the cost of carpet is $15 per square yard, therefore the cost of carpet for 12 square yards is,

hence, the cost of carpet is $180.

assuming the dimensions of the room be,

15 ft by 12 ft

so, the area of the floor of that room is,

we can convert 180 square feet into square yards, we know that,

1 sq ft = 0.111 sq yard

so, 180 square feet is,

so the area of floor is 20 square yards.

now, the cost of carpet is 15 dollars per square yard, therefore the cost of carpet for 20 square yards is,

so, it will cost $300.