ACT Practice - Coordinate Geometry

1.

Multiple Choice

2 mins

1 pt

Which of these lines would be parallel to the line

y-2x=7

?

$y=2x+3$

$y=3x+1$

$y=7x-2$

$y=9x+8$

$y=12x-1$

2.

Multiple Choice

2 mins

1 pt

How many units is the diameter of a circle with equation

\left(x-2\right)^2+\left(y-4\right)^2=64

?

2

4

8

12

16

3.

Multiple Choice

2 mins

1 pt

Which of the following gives the coordinates of the vertex of

y=2x^2-3

in the

xy

coordinate plane?

$\left(0,2\right)$

$\left(0,-3\right)$

$\left(2,-3\right)$

$\left(3,-2\right)$

$\left(6,0\right)$

4.

Multiple Choice

2 mins

1 pt

In the $xy$ coordinate plane, if one takes the x-coordinate of a point in the first quadrant and a y-coordinate of a point in the third quadrant and multiplies them together, the answer will be:

always negative

always positive

sometimes positive, sometimes negative

always zero

It cannot be determined with the given information

5.

Multiple Choice

2 mins

1 pt

In an 8-inch by 8-inch checkerboard, each square has an edge length of 1 inch. What is the distance from one corner of the board to the other corner that is diagonally opposite of it?

4

8

8\sqrt{2}

$8\sqrt{3}$

16

6.

Multiple Choice

2 mins

1 pt

What is the slope of line $y=-3x+2$ if reflected across the x-axis?

-3

$-\frac{3}{2}$

1

2

3

7.

Multiple Choice

2 mins

1 pt

The circle with a center C and the right triangle ABC intersect the x-axis at point B and the y-axis at point A. The length of the hypotenuse of $\Delta ABC$ is $6\sqrt{2}$ . What is the equation of circle C?

$x^2+y^2=6$

$\left(x-3\right)^2+\left(y-3\right)^2=9$

$\left(x+6\right)^2-\left(y+6\right)^2=12$

$\left(x-6\right)^2+\left(y-6\right)^2=36$

$\left(x-6\sqrt{2}\right)^2+\left(y-6\sqrt{2}\right)^2=36$

8.

Multiple Choice

2 mins

1 pt

If $g\left(t\right)=2t+2$ is graphed in the $xy$ coordinate plane and is shifted up 3 units and to the left 4 units, what equation would represent the new function?

$f\left(t\right)=2\left(t-2\right)$

$f\left(t\right)=2\left(t-3\right)+6$

$f\left(t\right)=2\left(t+4\right)+5$

$f\left(t\right)=2\left(t+3\right)+6$

$f\left(t\right)=2t^2+3$

9.

Multiple Choice

2 mins

1 pt

A triangle is formed by the line $x=3$ , which its longest side overlaps, and 2 other lines, one of which has a slope of 1 and the other of which is perpendicular to the line with the slope of 1. Which of the following could be the lengths of the 2 shorter sides of the triangle?

2, 3

4, 7

5, 5

6, 2

8, 9

10.

Multiple Choice

2 mins

1 pt

What is the closest approximation of the fraction of all points in the $xy$ plane that would satisfy the expression $y\ge2x+1$ or $y\le-\frac{1}{2}x-1$ ?

$\frac{1}{4}$

$\frac{1}{3}$

$\frac{1}{2}$

$\frac{2}{3}$

$\frac{3}{4}$

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