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 (a) x-axis

(-4, -2)

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. And our given point is negative 12, negative five. We recall from previous lessons that a rectangular coordinate system is going to have a vertical Y axis and a horizontal X axis. Those come together at the origin in the middle, they extend toward negative infinity and positive infinity. But because we are graphing negative 12, negative five, we can have our units marked off in units of five in multiples of five. So from the origin heading to the right on our X axis, we can label five 10, 15 and 20. And then similarly from the origin heading to the left along the X axis, we have a negative five, negative 10, negative 15. And if I could draw more evenly, no, a negative 20. And similarly, we'll mark along our Y axis from the origin going up, we'll have five, 10 and 15. And then from our origin heading down along the Y axis, we'll have negative five, negative 10 and negative 15. And then for the given point, we recall from previous lessons that the first value listed is our X value and then a comma and then our Y value. So our X value is negative 12 from the origin, we will go to the left 12 units. And then for our Y value of negative five, we will go down from that X value of negative 12, we'll go down five units and we can label that as negative 12, negative five. Now we are asked to plot the one that is symmetric with respect to the X axis. That means it's going to be on the opposite side of the X axis. So our X values are going to remain the same, the X value is going to remain negative 12, but it's our Y value that's going to change. In other words, we're going to replace Y with negative Y if our Y value is negative five, replacing that with a negative Y will have negative negative five, which is positive five. So our point that is symmetric with respect to the X axis is at negative 12 5 from the origin, we still go to the left 12 units and now we're going up five units and we can label that one as negative 12 5. And there are our two points. 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 (-4, -2)

Key Concepts

Symmetry with respect to the x-axis

Coordinate Plane

Plotting Points

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