Coordinate Geometry Hard

1. In the standard (x, y) coordinate plane, what is the equation of the line that passes through the origin and the point (3, 4)?

Y = 1/4x + 3/4

Y = 1/4x - 1/3

Y = 4/3x

Y = 1/2x + 3/4

Y = 9/4x

slope = 3/4. remember the origin is just the point (0, 0) so you can use the slope formula followed by point slope form: y - y1 = m(x - x1) but if you think about it, b has to be 0 if it goes through the origin!

Explanation

slope = 3/4. remember the origin is just the point (0, 0) so you can use the slope formula followed by point slope form: y - y1 = m(x - x1) but if you think about it, b has to be 0 if it goes through the origin!

2. A system of linear equations is shown below.

4y = 3x + 12
-4y = -3x - 8

Which of the following describes the graph of this system of linear equations in the standard (x, y) coordinate plane?

Two parallel lines with negative slope

Two parallel lines with positive slope

A single line with negative slope

A single line with positive slope

Two perpendicular lines

The solution is no solution (0 = 4) so the lines are parallel and the slope of each of them is positive 3/4 (in the second one, the two negatives cancel).

Explanation

The solution is no solution (0 = 4) so the lines are parallel and the slope of each of them is positive 3/4 (in the second one, the two negatives cancel).

3. What is the slope of the line that is perpendicular to the line determined by the equation 7x + 4y = 11?

-4

-7/4

11/4

4

4/7

Solve for y - then take the opposite reciprocal of the slope since the line is perpendicular

Explanation

Solve for y - then take the opposite reciprocal of the slope since the line is perpendicular

4. Given the vertices of parallelogram QRST in the standard (x, y) coordinate plane below, what is the area of triangle QRS, in square units?

24

28

48

60

80

Area triangle = 1/2bh and the base is 6 units (from -3 to 3) and the height is 8 units (from -5 to 3). 1/2*6*8= 24 sq units

Explanation

Area triangle = 1/2bh and the base is 6 units (from -3 to 3) and the height is 8 units (from -5 to 3). 1/2*6*8= 24 sq units

5. For what value of n would the following system of equations have an infinite number of solutions?

3a + b = 12
12a + 4b = 3n

4

9

16

36

48

For infinite solutions, every term in the second equation would have to be a multiple of each term in the first equation. The a and b terms are clearly multiplied by 4. 12*4 = 48. So your equation is 48 = 3n, solve for n.

Explanation

For infinite solutions, every term in the second equation would have to be a multiple of each term in the first equation. The a and b terms are clearly multiplied by 4. 12*4 = 48. So your equation is 48 = 3n, solve for n.

6. Given that y - 5 = 1/2x + 1 is the equation of a line, at what point does it cross the x-axis?

-15

-12

1

4

6

It crosses the x-axis when y = 0, so 0-5 = 1/2x + 1. solve for x and you should get the right answer.

Explanation

It crosses the x-axis when y = 0, so 0-5 = 1/2x + 1. solve for x and you should get the right answer.

7. In the standard (x, y) coordinate plane, if a square has the vertices (-2, -3), (2, -3) and (2, 1), what is the set of coordinates for the final vertex?

(2, -1)

(1, -2)

(-1, 2)

(-2, -1)

(-2, 1)

You just need to sketch this one to see it - don't try and figure it out in your head.

Explanation

You just need to sketch this one to see it - don't try and figure it out in your head.

8. In the standard (x, y) coordinate plane, if the x-coordinate of each point on a line is 5 more than half the y-coordinate, what is the slope of the line?

-5

-1/2

1/2

2

5

x = 1/2y + 5. Solve for y and you get y = 2x - 5. This one is hard!

Explanation

x = 1/2y + 5. Solve for y and you get y = 2x - 5. This one is hard!