ACT 1 Geo: Use coordinate methods

$Q_{1}:$ Given two lines in a coordinate plane: Line $A$ with equation $2x - 3y = 7$ and Line $B$ with equation $4x + 2y = 12$. What can you conclude about the relationship between these lines?

$Q_{2}:$ If two lines in a coordinate plane, Line $P$ and Line $Q$, are perpendicular, what can be said about their slopes?

$Q_{3}:$ Two lines in a coordinate plane are given by the equations: Line $M$: $3x + 4y = 12$ Line $N$: $6x - 8y = 24$. Are these lines are?

$Q_{4}:$ Given the coordinates of four points $A(2, 3),$ $B(4, 1),$ $C(6, 5),$ and $D(8, 3)$, which of the following best describes the quadrilateral formed by connecting these points?

$Q_{5}:$ In a coordinate plane, two sides of a quadrilateral have slopes of $-2$ and $\frac{1}{2}$, respectively. If these two sides are not parallel, what type of quadrilateral can be formed by connecting these sides?

$Q_{6}:$ Two lines in a coordinate plane are given by the equations: Line $X: 2x - 5y = 10$. $Line Y: 4x - 10y = 20$. What can you conclude about the relationship between these lines?

$Q_{7}:$ Given a quadrilateral with vertices at $A(1, 2),$ $B(4, 5)$, $C(7, 2),$ and $D(4, -1),$ what type of quadrilateral is formed by connecting these points?

$Q_{8}:$ If the slopes of two sides of a quadrilateral are equal, what type of quadrilateral is it most likely to be?

$Q_{9}:$ Two lines in a coordinate plane are given by the equations: Line $P: 3x - 4y = 12$. Line $Q: 6x - 8y = 18$. What can you conclude about the relationship between these lines?

$Q_{10}:$ If two sides of a quadrilateral are parallel and equal in length, what type of quadrilateral is it most likely to be?

$Q_{11}:$ If two sides of a quadrilateral are parallel and the other two sides are not parallel or equal in length, what type of quadrilateral is it most likely to be?

$Q_{12}:$ Given the equations of two lines, $C: 2x - 3y = 6$ and $B: 4x + y = 2$, which of the following is true?

$Q_{13}:$ If the slopes of two lines are equal, what type of quadrilateral can be formed by these lines?

$Q_{14}:$ Given two intersecting lines, what geometric relationship is necessary for them to form a quadrilateral?

$Q_{15}:$ If the slopes of two lines are negative reciprocals of each other, what type of quadrilateral can be formed by these lines?

$Q_{16}:$ Which of the following statements is true about the diagonals of a rectangle?

$Q_{17}:$ What is the condition for two lines to be parallel when given in slope-intercept form $(y = mx + b)$?

$Q_{18}:$ If the slopes of two lines are both zero, what type of quadrilateral can they form?

$Q_{19}:$ Given the equations of two lines, $L_{1}: 3x - 2y = 4$ and $L_{2}: 6x - 4y = 8$, what is the relationship between these lines?

$Q_{20}:$ When do two lines in the coordinate plane not form a quadrilateral?

$Q_{21}:$ What is the condition for two lines to be perpendicular when given in slope-intercept form $(y = mx + b)$?

$Q_{22}:$ If two lines are parallel and one of them passes through the midpoint of the other, what type of quadrilateral is formed?

$Q_{23}:$ Given the equations of two lines, $L_{1}: 2x + 3y = 6$ and $L_{2}: 4x + 6y = 12$, what can be concluded about the relationship between these lines?

$Q_{24}:$ If two lines are skew lines in three-dimensional space, what type of quadrilateral do they form?

$Q_{25}:$ What geometric condition must be met for a quadrilateral to be classified as a parallelogram?

$Q_{26}:$ If the diagonals of a quadrilateral bisect each other and are perpendicular to each other, what type of quadrilateral is formed?If the diagonals of a quadrilateral bisect each other and are perpendicular to each other, what type of quadrilateral is formed?