Video: AQA GCSE Mathematics Foundation Tier Pack 4 β€’ Paper 2 β€’ Question 16

The following equations represent straight lines on the graph. circle the equation of the line which reflects shape A onto shape B. [A] 𝑦 = 0 [B] π‘₯ = 0 [C] 𝑦 = 1 [D] π‘₯ = 1

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Video Transcript

The following equations represent straight lines on the graph. circle the equation of the line which reflects shape A onto shape B.

Well, to enable us to find the mirror line or the line of reflection between our two shapes, the first thing we should do is count number of squares between the shapes. Well, we can see that there are four squares between our two shapes. And our mirror line is always halfway between the two shapes or the reflection of the shape and the original shape. So therefore, we want the mirror line where I’ve drawn in blue because this is two units or two squares on our graph away from B and two squares away from A. So now, what we need to do is find the equation of this line.

So to find the equation of this line, well we know that because it’s a horizontal line, it’s gonna be 𝑦 is equal to. That’s because a horizontal line runs through the 𝑦-axis. And the 𝑦-coordinates along this line will never change; they will stay the same. There will only be the π‘₯-coordinates to change. And we can see with this mirror line that if we take a look at the axis and see where it crosses the 𝑦-axis, so the vertical axis, this is it, one. So therefore, the 𝑦-coordinate on this line is always one. So we can say that 𝑦 must be equal to one. So therefore, the equation of the line which reflect shape A onto shape B is 𝑦 is equal to one. But let’s take a quick look at the other lines to see what these would be.

Well, if we drew the line 𝑦 equals zero, well this would be too close to B because it’ll be one square away from B but three squares away from A. And if we drew π‘₯ is equal to zero, well this would just be on the 𝑦-axis because this is where the π‘₯-coordinate is zero. And π‘₯ is equal to one. Well, these are both vertical lines and our reflection is a horizontal reflection. So therefore, these could not be correct. So the equation 𝑦 equals one is the correct equation of the mirror line or the line of reflection from shape A onto shape B.

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