1.) Given points A(-4, 5), B(2, 3), C(0, 4) and D(5, 0), decide if AB and CD are parallel, perpendicular or neither.

=Neither

2.)Given the equations y = 1x + 7 and y = 3x - 2, decide whether the lines are parallel, perpendicular or neither.
=neither

3.) Given the equations y = 4/3x - 3 and y = -3/4x + 2, decide whether the lines are parallel, perpendicular, or neither.
=Perpendicular

4.) Which set of points are collinear?{options being A(-1,5); B(2,6); C(4,7), A(0,0); B(1/2,3); C(1,5), A(-4,-2); B(0,-4); C(2,-5)
= A(-4,-2); B(0,-4); C(2,-5)

5.)Choose whether the lines given below are parallel, perpendicular or neither.
4x - 6y = 9; 4y + 6x = 12
=perpendicular

6.) Choose whether the lines given below are parallel, perpendicular or neither.4x - 6y = 9; 3x - 2y = 11
=neither

7.) Triangle ΔABC has vertices A(2,5), B(8,1) and C(-2,-1) and is a right triangle. If the slope of AB is -2/3 and the slope of AC is 3/2, are the lines parallel, perpendicular or neither?
=perpendicular

Out of 30 questions these few I struggled with. I put what I feel was right but to be sure I would like some one to check my answers and if there wrong redirect me on how to get the correct answer.( after the = is the answer i think it is.

All your answers are correct.

Thanks:)

To determine if two lines are parallel, perpendicular, or neither, we need to compare their slopes.

1.) To find the slope of line AB, we can use the formula: slope = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are two points on the line.
Slope of AB = (3 - 5) / (2 - (-4)) = -2 / 6 = -1/3

To find the slope of line CD, we can use the same formula.
Slope of CD = (0 - 4) / (5 - 0) = -4 / 5

Since the slopes of AB and CD are not equal, they are not parallel.
Also, the product of their slopes is not -1, so they are not perpendicular.
Therefore, AB and CD are neither parallel nor perpendicular.

2.) The given equations are in the form y = mx + b, where m represents the slope.
Comparing the equations, we can see that the slopes are different (1 and 3).
Since the slopes are not equal, the lines are not parallel.
Also, the product of the slopes is not -1, so they are not perpendicular.
Therefore, the lines y = 1x + 7 and y = 3x - 2 are neither parallel nor perpendicular.

3.) Comparing the equations, we can see that the slopes are negative reciprocals of each other (-3/4 and 4/3).
Since the slopes are negative reciprocals, the lines are perpendicular.
Therefore, the lines y = 4/3x - 3 and y = -3/4x + 2 are perpendicular.

4.) To determine if the points are collinear, we can calculate the slopes of the lines formed by the points AB, BC, and AC.
Slope of AB = (6 - 5) / (2 - (-1)) = 1/3
Slope of BC = (7 - 6) / (4 - 2) = 1/2
Slope of AC = (-2 - 5) / (-4 - 2) = 1

Since the slopes of AB, BC, and AC are equal (1/3, 1/2, and 1), the points A, B, and C are collinear.

5.) The given equations 4x - 6y = 9 and 4y + 6x = 12 can be rewritten in the form y = mx + b.
For the first equation, rearranging the terms, we get y = (4/6)x - (9/6).
The slope of the first equation is 4/6, which simplifies to 2/3.

For the second equation, rearranging the terms, we get y = (-4/6)x + (12/6).
The slope of the second equation is -4/6, which simplifies to -2/3.

Since the slopes of the two equations are negative reciprocals (-2/3 and 2/3), the lines are perpendicular.

6.) Comparing the equations 4x - 6y = 9 and 3x - 2y = 11, we can see that their slopes (coefficients of x) are different.
Since the slopes are not equal, the lines are not parallel.
Also, the product of the slopes is not -1, so they are not perpendicular.
Therefore, the lines 4x - 6y = 9 and 3x - 2y = 11 are neither parallel nor perpendicular.

7.) Given the points A(2,5), B(8,1), and C(-2,-1), we can find the slopes of AB and AC.
Slope of AB = (1 - 5) / (8 - 2) = -4 / 6 = -2/3
Slope of AC = (-1 - 5) / (-2 - 2) = -6 / -4 = 3/2

Since the slopes of AB and AC are negative reciprocals (-2/3 and 3/2), the lines are perpendicular. Therefore, the lines formed by A(2,5)-B(8,1) and A(2,5)-C(-2,-1) are perpendicular.