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. (-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 origin on a rectangular coordinate system, our given point is negative 12, negative five. Then for our answer choices, we are given four rectangular coordinate systems. All four of them have a vertical Y axis and a horizontal X axis which come together at the origin answer. Choice A has a range for the Y axis from negative 15 to positive 10 in the domain for the X axis from negative 20 to positive 15. It has points marked at negative 12, negative five and negative 12 5. Answer choice B has a range for the Y axis from negative 10 to positive 10. And the domain for the X axis is from negative 20 to positive 15. It has a point drawn at negative 12, negative five and another one at 12 5. Answer choice C has a range for its Y axis from negative 10 to positive 10. And the domain for the X axis from negative 20 to positive 15, it has a point drawn at negative 12, negative five and another point drawn at 12, negative five. And answer choice D has a range for the Y axis from negative 15 to positive 10. And the domain for the X axis is from negative 20 to positive 15. It has a point at negative 12, negative five and another point at five, negative 12. Now, even if we didn't have our point drawn for us, we would know where to plot it because we recall from previous lessons that an ordered pair tells us first, the X value for a point and then the Y value for that point. So if we've got our vertical Y axis, horizontal X axis, they come together the origin for our X values, the negative X values are to the left of the origin and the positive X values are to the right of the origin for the Y values. The positive Y values are above the origin and the negative Y values are below the origin. So if we have an X value of negative 12 from the origin, we're going to head left 12 units for the X value of negative 12 and for a Y value of negative five, from that X value, we're going to head down five units for a negative five. And that will give us our point negative 12, negative five. Now to plot a point that is symmetric with respect to the origin, what we're going to do is replace our X value with a negative X value and our Y value with a negative Y value. And so since our X value is negative 12, that's going to be a negative negative 12. And since our Y value in the given point was negative five in the one with respect to the origin reflected over the origin symmetric over the origin, it's going to be a negative negative five. And now we need to simplify that negative negative 12 is positive 12 and negative negative five is positive five. So even though with respect to the origin, we're taking the negatives of our given, they end up being the positives because we were given to negative values. Now plotting the point from the origin, we're going to move to the right 12 units for X value of positive 12. And then we're going to go up five units for our Y value of positive five. And there is our 0.12 5. We look at our answer choices and this matches with answer choice B 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. (-4, -2)

Key Concepts

Coordinate Plane and Plotting Points

Symmetry with Respect to the Origin

Reflection and Transformation in the Coordinate Plane

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