Here, the trapezoid is rotating about a point on the base of the trapezoid.īut on the ACT, you'll almost always be asked to rotate an object "about the origin." This means that the origin (coordinates $(0,0)$) acts as your center of rotation. Or the same shape can also be rotated about a different point. We can have an object that rotates about its own center.Ī trapezoid is rotating about its center. Let us look at a visual demonstration of this. This center point of our rotation can be anywhere on the coordinate plane or on the shape in question (notice that it does NOT have to be the center of the shape). We must always select a point to act as the center point for our rotation.
Imagine that we can adjust the object with our hands-it will spin, while still lying flat, like a piece of paper on a tabletop. Objects in the coordinate plane can also be rotated (turned) clockwise or counterclockwise. Nature's take on lines of symmetry in action. If we count them as they are, we can see that there are eight lines of symmetry total. Now we can count the lines of symmetry without fear that we are double-counting one line. Here, we have gotten rid of the other half of each line of symmetry and transformed them into all the radii of the circle. The number of actual lines of symmetry will be half the number of connecting points, because we need to only count each line one time.īecause this is a busy figure, let us look at it a little more simplistically. Now, from here, we can see that there are also lines of symmetry between our interior angles, like so:īut wait! We can count our total number of lines (diameters, since they're spanning the entire length of the circle), but we CANNOT count each individual point that connects to the circumference of the circle as a line of symmetry. If we connect opposite angles in our figure, we will have several lines of symmetry. This means that each side must be a reflection of the other, about a line. To find our lines of symmetry, we must divide our figure into symmetrical halves. Let's look at a typical ACT line of symmetry problem.
This line, about which the object is reflected, is called the "line of symmetry." Any point or shape can be reflected across the x-axis, the y-axis, or any other line, invisible or visible. So if you’ve got a solid grasp of all your foundational math topics (or you just really, really like coordinate geometry), then lets talk reflections, rotations, and translations!Ī reflection in the coordinate plane is just like a reflection in a mirror. Remember, each question is worth the same amount of points, so it is better that you can answer three or four questions on integers, triangles, or slopes than to answer one question on rotations. If you’re shooting for a perfect or nearly perfect score and want to make sure you have all your bases covered, then this is the guide for you.īut if you still need to brush up on your fundamentals, then your focus will be better spent on studying the more common types of math problems you’ll see on the test. Reflection, rotation, and translation problems are fairly rare on the ACT, only appearing once per test, if at all. This will be your complete guide to rotations, reflections, and translations of points, shapes, and graphs on the ACT-what these terms mean, the types of questions you’ll see on the test, and the tips and formulas you’ll need to solve these questions in no time. And, often enough, you’ll be asked to do so on the ACT.
Reflections, rotations, translations, oh my! Whether you’re dealing with points or complete shapes on the coordinate plane, you can spin 'em, flip 'em, or move 'em around to your heart’s content.