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 (a) x-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 X axis on a rectangular coordinate system. Our given point is 17, negative 28. All right. So we need to recall from previous lessons. A rectangular coordinate system has a vertical Y axis and a horizontal X axis that's not very horizontal. A horizontal X axis, they come together at the origin in the middle and they extend toward negative infinity on the left and positive infinity on the right for the X axis. But here are X value we see looking at our point, we recall that the X value is given first and then the Y value the X value here is a positive 17. So we want to have our units match where 17 is getting toward the upper limit of our units that we're marking along the X axis. So from the origin, we can count by five, we can mark a positive five, a positive 10, a positive 15 and a positive 20. And then to the left of the origin, we're heading toward negative infinity. And we can also mark negative five, negative 10. And I only drew so far as negative 15 along our X axis. Now, for our Y axis, we see that our Y value is a negative 28. So we could mark those skipping by tens. For the Y values below the origin are the negative numbers. We have a negative 10, a negative 20 a negative 30. And then above the origin, we can also mark a positive 10, positive 20 a positive 30. And now that's what we've chosen the scale of our rectangular coordinate system to be. Now to plot our point, we know that 17 is the X value. So from the origin, we go to the right 17 units. And then from that X value of 17, we see our Y value is negative 28. So we're going to go down 28 units and this is our 0.17 negative 28. Now we're also asked to plot the point symmetric to the given point with respect to the X axis. So in other words, it's going to be on the other side of the X axis but symmetric. And the way we do that is we replace why with negative Y. So if our Y value is negative 28 we're going to replace it with a negative negative 28 which is the same as a positive 28 the X value remains 17 plotting the 0.17 28 from the origin, we go to the right 17 units for our X value. And from there we'll go up 28 units for our Y value. And there is 17 28 on our rectangular coordinate system. 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 (a) x-axis (5, -3)

Key Concepts

Coordinate Plane and Plotting Points

Symmetry with Respect to the x-axis

Reflection of Points

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