ACT Practice - Coordinate Geometry

Which of these lines would be parallel to the line

 $y-2x=7$  ?

•  $y=2x+3$  

•  $y=3x+1$  

•  $y=7x-2$  

•  $y=9x+8$  

•  $y=12x-1$  

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

Which of the following gives the coordinates of the vertex of

 $y=2x^2-3$  in the  $xy$  coordinate plane?

•  $\left(0,2\right)$  

•  $\left(0,-3\right)$  

•  $\left(2,-3\right)$  

•  $\left(3,-2\right)$  

•  $\left(6,0\right)$  

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

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

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

• -3

•  $-\frac{3}{2}$  

• 1

• 2

• 3

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?

•  $x^2+y^2=6$  

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

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

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

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

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?

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

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

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

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

•  $f\left(t\right)=2t^2+3$  

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

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

•  $\frac{1}{4}$  

•  $\frac{1}{3}$  

•  $\frac{1}{2}$  

•  $\frac{2}{3}$  

•  $\frac{3}{4}$