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.(-4, -2)

Accepted Answer

Welcome back. I am so glad you're here. We are asked to draw the given point and one symmetric to the given point with respect to the Y axis 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 of them have a vertical Y axis. A horizontal X axis. Those come together at the origin for answer choices A and D. The range for what's drawn for our Y axes are from negative 15 to positive 10. And the domain for what's drawn for our X axis is from negative 20 to positive 15. And then for answer choices B and C, the range for what's drawn for our Y axis is from negative 10 to positive 10. And the domain for what's drawn for our X axis is from negative 20 to positive 15. Answer choice A has two points marked one at negative 12, 5 and one at negative 12, negative five. Answer choice B has two points negative 12, negative five and 12 5. Identified answer choice C has the points negative 12, negative five and 12, negative five. And answer choice D has the points negative 12, negative five and five, negative 12. All right. Even though these have been plotted already, we would know where to plot our given point negative 12, negative five. Because we know that for an ordered pair for a point, the first number given is always the X value and the second number given is always the Y value. So on our rectangular coordinate system, we have that vertical Y axis, the horizontal X axis, they come together at the origin. The negative numbers for the X values are always to the left of the origin. And the positive numbers for the X values are always to the right of the origin. The positive numbers for the Y values are always above the origin. And the negative numbers for the Y values are always below the origin. So when we have that first X point or the X value for our point at negative 12, from the origin, we're going to head to the left 12 units and that will be a negative 12. But we still need to move our Y values, we have a Y value of negative five. So from that X value of negative 12, we'll head down five units and then we'll be at the point negative 12, negative five. Now, the second thing we're asked to do is to find the point that is symmetrical with respect to the Y axis. In order to do that, we're going to take our point. And instead of having our X value, we're going to have a negative X value and then our Y value will remain the same. So because our X value is negative 12, we'll now have a negative negative 12. And then our Y value remains the same Y was negative five. So that remains negative five. And to simplify this, a negative negative 12 is a positive 12 and negative five remains the Y value. So our point is at 12, negative five when it is reflected over the Y axis. So to plot this one, we have our X values now positive. So from the origin, we go to the right 12 units. But then for our Y value of negative five, we still go down five units and there's our 0.12 negative five, we look at our answer choices and this matches with answer choice. C 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.(-4, -2)

Key Concepts

Symmetry with respect to the y-axis

Coordinate Plane

Plotting Points

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