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goblinko [34]
3 years ago
15

-2x + 3y = 6

SAT
2 answers:
spin [16.1K]3 years ago
6 0

Answer:

-2\cdot x + 3\cdot y = 6 is perpendicular to 3\cdot x + 2\cdot y = 6. (Answer: A)

Explanation:

From Linear Algebra, we know that two vectors are perpendicular to each other when its Dot Product equals zero. In addition, a linear equation can be rewritten in this manner:

a\cdot x + b\cdot y = c

(a, b)\, \bullet \, (x,y) = 0

Where (a,b) is the vector generator.

Then, if two lines are perpendicular to each other, then the dot product of respective vector generators must be zero. That is to say:

(a, b) \, \bullet \, (c, d) = 0

We proceed to check each case:

A) (a, b) = (-2, 3), (c, d) = (3, 2)

D.P. = (-2)\cdot (3) + (3)\cdot (2)

D.P. = 0

B) (a, b) = (-2, 3), (c, d) = (3, 4)

D.P. = (-2)\cdot (3) + (3)\cdot (4)

D.P. = 6

C) (a, b) = (-2, 3), (c, d) = (2, 4)

D.P. = (-2)\cdot (2) +(3)\cdot (4)

D.P. = 8

D) (a, b) = (-2, 3), (c, d) = (2, 6)

D.P. = (-2)\cdot (2) + (3) \cdot (6)

D.P. = 14

Which coincides with image attached below.

-2\cdot x + 3\cdot y = 6 is perpendicular to 3\cdot x + 2\cdot y = 6. (Answer: A)

Archy [21]3 years ago
3 0

Answer:

The answer is A.

Explanation:

The perpendicular equation has a slope of the negative reciprocal. If we put the equation in slope-intercept form (y=mx+b), we can see the given equation's slope is 2/3. Therefore, the reciprocal must have a slope of -3/2 in slope intercept form (y= -3/2x+b).

Multiplying both sides of the equation by 2 to cancel the denominator, we have 2y = -3x +b. Then, move the -3 to the left side of the equation making the value positive, and we have 2y +3x = b. Therefore, A is the correct answer.

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