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

Question

Concept Check Plot each point, and then plot the points that are symmetric to the given point with point with respect to the (c) origin. (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 origin on a rectangular coordinate system. Our given point is 17, negative 28. And then we have four answer choices that give us four rectangular coordinate systems. All four of the rectangular coordinate systems have vertical Y axis, horizontal X axis. They come together with the origin, our X axis has a domain of negative 20 to positive 20 for what's drawn and it's marked off in increments of five. And the range for what's drawn for our Y axis is from negative 30 to positive 40. And that one is also marked off in increments of five. For answer choice A we have a point drawn at negative 1728 and 17, negative 28. For answer choice B we have a point drawn at negative 1728 and 1728. Answer choice C we have a point drawn at negative 17, negative 28 and a point drawn at 1728. And answer choice D we have a point drawn at 1728 and 17, negative 28. All right. So our given points, our given point is 17, negative 28. Now, even if we didn't have these answer choices drawn for us, we know where to look for 17 and negative 28. Because the first value is always our X value and the second value is always our Y value. So on the rectangular coordinate system, if we have that vertical Y axis and horizontal X axis, the positive X numbers are always to the right of the origin where it comes together and the negative X values are always to the left of the origin. Our X value is a positive 17. So that means it's going to be to the right of the origin 17 units. Now we can mark off where 17 is to the right of the origin on the X axis. But we still have to move the Y coordinate up or down. Our given Y coordinate is negative 28. The Y coordinates are always positive above the X axis above the origin and the Y coordinates are always negative below the origin. So our negative 28 is going to be down below the origin for the Y values. And the specific 0.17 negative 28 is where those two come together. So that's down here in the fourth quadrant down into the right of our origin and we can label that 17 negative 28. Now the other spot is going to be drawn symmetrical with respect to the origin. The way that we do that is we are going to put in for our X value A negative X and for our Y value A negative Y. So our original X value is positive 17. Now we're going to have a negative 17. Our original Y value is negative 28. We're going to have a negative negative 28 or in other words, it's going to be negative 17 for the X value and negative negative 28 is a positive 28 for the Y value. So from the origin, our X value is negative 17, we go to the left 17 units and then our Y value is positive 28 we go up 28 units and there we have our negative 1728 the point that is symmetrical with respect to the origin. Now we look at our answer choices and the one that matches with this is 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 (c) origin. (5, -3)

Key Concepts

Coordinate Plane and Plotting Points

Symmetry with Respect to the Origin

Reflection and Transformation in the Coordinate Plane

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