Concept Check Plot each point, and then plot the points that are ...

Question

Concept Check Plot each point, and then plot the points that are symmetric to the given point with point with respect to the (b) y-axis(5, -3)

Accepted Answer

Welcome back. I am so glad you're here. We are asked to draw the given point and the one symmetric to the given point with respect to the Y axis on a rectangular coordinate system. Our given point is 17, negative 28. Then for our answer choices, we are given four drawings with rectangular coordinate grids. All four of them have a vertical Y axis, a horizontal X axis. And those come together at the origin in the middle. The X axis has a domain of what's drawn of negative 20 to positive 20 marked off in increments of five. And the Y axis has a range of what's drawn from negative 30 to positive 40. And those are also marked off in increments of five. Answer choice A has a point marked at negative 17, negative 28 and a point marked at 17, negative 28. Answer trace B has a point marked at negative 1728 and 1728. Answer choice C has a point marked at negative 17, negative 28 and 1728. And answer choice D has a point marked at 1728 and 17, negative 28. All right. So even if we didn't have those answer choices to look at, we would know where to find our 17, negative 28. Because we know that an ordered pair for a point always gives us our X value first followed by our Y value. So if we draw another quick sketch of a coordinate plane, we'll have that vertical Y axis, the horizontal X axis, they come together at the origin in the middle. The negative X values are always found to the left of the origin. And the positive X values are always found to the right of the origin. The negative Y values are always found below the origin. And the positive Y values are always found above the origin. And so if we've got an X value of positive 17, we're going to start at the origin and go to the right for our positive 17 X value 17 units and we can mark that so positive 17. And then for our Y value, it's a negative 28. So we'll go below the origin, go down 28 units and where those two come together 17 for the X value and negative 28 for the Y value. That's our 0.17 negative 28. Now, for the part where it has to, our second point needs to be reflected over the Y axis, what that means is that we are going to have instead of our X value, we're going to put that in, put in a negative for our X value and we'll keep our Y value the same. So our X value for our given point was 17. The negative of that would be negative 17, our Y value is negative 28. It remains negative 28. That's going to give us reflection over the Y axis. So let's plot this point from the origin for our X value will go to the left 17 units. And for our Y value, we'll go down 28 units and that will be the point negative 17, negative 28. And so we look for those two points in our answer choices and that matches with the answer choice. A well done. We'll catch you on the next one.

Concept Check Plot each point, and then plot the points that are symmetric to the given point with point with respect to the (b) y-axis(5, -3)

Key Concepts

Symmetry with Respect to the Y-Axis

Coordinate Plane

Plotting Points

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