Quiz about ACT - Coordinate Geometry

Question 1

In the standard $$\left(x,y\right)$$ coordinate plane, the point $$\left(2,1\right)$$ is the midpoint of $$\overline{CD}$$ . Point $$C$$ has coordinates $$\left(6,8\right)$$ . What are the coordinates of point $$D$$ ?

Accepted Answer

$$\left(-2,-6\right)$$

Answer

$$\left(-2,-\frac{7}{2}\right)$$

Answer

$$\left(4,\frac{9}{2}\right)$$

Answer

$$\left(10,10\right)$$

Answer

$$\left(10,15\right)$$

Question 2

What is the slope of a line, in the standard $$\left(x,y\right)$$ coordinate plane, that is parallel to $$x+5y=9$$ ?

Accepted Answer

$$-\frac{1}{5}$$

Answer

$$-5$$

Answer

$$\frac{1}{5}$$

Answer

$$\frac{9}{5}$$

Answer

$$9$$

Question 3

In the standard $$\left(x,y\right)$$ coordinate plane, a circle with its center at $$\left(8,5\right)$$ and a radius of $$9$$ coordinate units has which of the following equations?

Accepted Answer

$$\left(x-8\right)^2+\left(y-5\right)^2=81$$

Answer

$$\left(x-8\right)^2+\left(y-5\right)^2=9$$

Answer

$$\left(x+8\right)^2+\left(y+5\right)^2=81$$

Answer

$$\left(x+8\right)^2+\left(y+5\right)^2=9$$

Answer

$$\left(x+5\right)^2+\left(y+8\right)^2=81$$

Question 4

Regardless of how the graph is oriented in the standard $$\left(x,y\right)$$ coordinate plane, NO graph in one of the following categories has a vertical line of symmetry. Which one?

Accepted Answer

Scalene Triangle

Answer

Line

Answer

Square

Answer

Pentagon

Answer

Parallelogram

Question 5

The quadratic function $$f$$ and $$\Delta MPQ$$ are graphed in the standard $$\left(x,y\right)$$ coordinate plane below. Points $$M\left(2a,5b\right)$$ , $$N\left(4a,9b\right)$$ , and $$P\left(6a,5b\right)$$ are on $$f$$ . Point $$Q\left(4a,0\right)$$ is NOT on $$f$$ . In terms of $$a$$ and $$b$$ , what is the area, in square coordinate units, of $$\Delta MPQ$$ ?

Accepted Answer

$$10ab$$

Answer

$$8ab$$

Answer

$$12ab$$

Answer

$$15ab$$

Answer

$$20ab$$

Question 6

In one of the following graphs in the standard $$\left(x,y\right)$$ coordinate plane, the solution set to the system of inequalities below is shown shaded. Which one?

$$x+2y\le6$$

$$3x^2>12-3y^2$$

Accepted Answer

Option E is correct

Answer

A.

Answer

B.

Answer

C.

Answer

D.

Question 7

In the standard $$\left(x,y\right)$$ coordinate plane, what is the slope of the line through $$\left(-3,1\right)$$ and $$\left(5,6\right)$$ ?

Accepted Answer

$$\frac{5}{8}$$

Answer

$$-\frac{5}{2}$$

Answer

$$-\frac{5}{8}$$

Answer

$$\frac{5}{2}$$

Answer

$$\frac{7}{2}$$

Question 8

Quadrant I of the standard $$\left(x,y\right)$$ coordinate plane is shown on a large computer screen. A blinking dot is positioned at $$\left(2,3\right)$$ . The dot makes exactly 2 moves: first, horizontally in the positive $$x$$ direction for 4 seconds at a speed of $$0.5$$ coordinates per second; then, vertically in the positive $$y$$ direction for 2 seconds at the same speed. At what point is the dot located after these 2 moves?

Accepted Answer

$$\left(4,4\right)$$

Answer

$$\left(2,6\right)$$

Answer

$$\left(3,5\right)$$

Answer

$$\left(5,3\right)$$

Answer

$$\left(6,5\right)$$

Question 9

In the standard $$\left(x,y\right)$$ coordinate plane below, point $$A$$ has coordinates $$\left(2,-4\right)$$ , and point $$B\left(8,-1\right)$$ divides $$\overline{AC}$$ so that the ratio $$AB:BC$$ is $$1:3$$ . What are the coordinates of point $$C$$ ?

Accepted Answer

$$\left(26,8\right)$$

Answer

$$\left(-16,-13\right)$$

Answer

$$\left(10,0\right)$$

Answer

$$\left(14,2\right)$$

Answer

$$\left(32,11\right)$$

Question 10

The point $$\left(4,r\right)$$ lies on the graph of $$y=-3x+2$$ in the standard $$\left(x,y\right)$$ coordinate plane. What is the value of $$r$$ ?

Accepted Answer

$$-10$$

Answer

$$-4$$

Answer

$$-14$$

Answer

$$-18$$

Answer

$$-24$$

Question 11

Which of the following equations is that of a line parallel to the line with the equation $$y=\frac{2}{3}x+4$$ in the standard $$\left(x,y\right)$$ coordinate plane?

Accepted Answer

$$y=\frac{2}{3}x+7$$

Answer

$$y=-\frac{3}{2}x+4$$

Answer

$$y=-\frac{3}{2}x+7$$

Answer

$$y=-\frac{2}{3}x+4$$

Answer

$$y=\frac{3}{2}x+4$$

Question 12

When graphed in the standard $$\left(x,y\right)$$ coordinate plane, the line with the equation $$\frac{5}{2}x+\frac{3}{4}y=-\frac{1}{2}$$ has a slope of:

Accepted Answer

$$-\frac{10}{3}$$

Answer

$$-\frac{3}{10}$$

Answer

$$-\frac{2}{3}$$

Answer

$$-\frac{15}{8}$$

Answer

$$-\frac{5}{2}$$

Question 13

Triangles $$\Delta ABC$$ and $$\Delta A$$ are graphed in the standard $$\left(x,y\right)$$ coordinate plane below. Triangle $$\Delta A$$ is the image of $$\Delta ABC$$ under one of the following transformations. Which one?

Accepted Answer

Reflection across the y-axis

Answer

$$90\circ$$ clockwise rotation about the origin

Answer

$$90\circ$$ counterclockwise rotation about the origin

Answer

Horizontal translation

Answer

Reflection across the x-axis

Question 14

In the standard $$\left(x,y\right)$$ coordinate plane, the 3 distinct points $$A\left(3,5\right)$$ , $$B\left(6,8\right)$$ , and $$C$$ are collinear, and $$B$$ is equidistant from $$A$$ and $$C$$ . What are the coordinates of $$C$$ ?

Accepted Answer

$$\left(9,11\right)$$

Answer

$$\left(4,7\right)$$

Answer

$$\left(1.5,1.5\right)$$

Answer

$$\left(4.5,6.5\right)$$

Answer

$$\left(7.5,10.5\right)$$

Question 15

In the standard $$\left(x,y\right)$$ coordinate plane below, the endpoints of the major and minor axes of the ellipse are labeled. Which of the following equations determines the ellipse?

Accepted Answer

$$\frac{x^2}{16}+\frac{y^2}{49}=1$$

Answer

$$\frac{x^2}{4}+\frac{y^2}{7}=1$$

Answer

$$\frac{x^2}{8}+\frac{y^2}{14}=1$$

Answer

$$\left(x-4\right)^2+\left(y-7\right)^2=1$$

Answer

$$\left(x+4\right)^2\left(y+7\right)^2=1$$

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