Given the four equations: (1) &3y-2x=12, (2) &-2x-3y=10, (3) &3y+2x=12, (4) &2y+3x=10. The pair representing perpendicular lines is:

1963 AMC 12 Problem 7

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Given the four equations:

\begin{aligned} (1)\quad&3y-2x=12,\\ (2)\quad&-2x-3y=10,\\ (3)\quad&3y+2x=12,\\ (4)\quad&2y+3x=10. \end{aligned}

The pair representing perpendicular lines is:

(1)

and

(4)

(1)

and

(3)

(1)

and

(2)

(2)

and

(4)

(2)

and

(3)

Rewrite each equation in slope-intercept form

Perpendicular nonvertical lines have slopes whose product is

-1

Line

(1)

has slope

\frac{2}{3},

and line

(4)

has slope

-\frac{3}{2}.

Their product is

-1,

so these two lines are perpendicular.

Thus, the correct answer is A.