Video: AQA GCSE Mathematics Higher Tier Pack 4 • Paper 3 • Question 4

𝐴 is the point (4, 10) and 𝐵 is the point (6, 2). Circle the midpoint of 𝐴𝐵. [A] (2, 8) [B] (5, 6) [C] (1, 4) [D] (5, 3)

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Video Transcript

𝐴 is the point four, 10 and 𝐵 is the point six, two. Circle the midpoint of 𝐴𝐵. The options are: two, eight; five, six; one, four; and five, three.

So in this problem, what we’re trying to do is find the midpoint between two points that we’ve been given. And those points are point 𝐴 and point 𝐵. And I’ve marked them on my sketch here of a graph. So we need to find the middle point between them. So how are we going to do that? Well, there is a formula that we can use to help us. And that formula is that the midpoint is equal to — then for our 𝑥-coordinate, it’s going to be 𝑥 one plus 𝑥 two over two. So that’s the two 𝑥-coordinates of the points added together then divided by two. And then for the 𝑦-coordinate, it’s 𝑦 one plus 𝑦 two over two. Again, that’s our two 𝑦-coordinates of the points added together then divided by two.

So if we take a look at our points, we’ve got four, 10 for 𝐴 and six, two for 𝐵. So what I’ve done is I’ve labeled them 𝑥 one, 𝑦 one and 𝑥 two, 𝑦 two. So, therefore, to calculate the midpoint, we’re gonna have it equal to four plus six over two, for the 𝑥-coordinate, because that’s 𝑥 one plus 𝑥 two over two. And then for the 𝑦-coordinate, we’re gonna have 10 plus two over two. And this is gonna give us the coordinates five, six. And that’s because we’ve got four plus six, which is 10, divided by two, which is five. And then we’ve got 10 plus two, which is 12, divided by two, which is six.

So we can check by having a look at our sketch. And I’ve marked the cross on our sketch. And you see that that looks like the midpoint. So that would be correct. And also, we can check that it’s sensible because we can think, right, our 𝑥-coordinates are four and six. Well, what’s between this? Well, the answer is five. Our 𝑦-coordinates are 10 and two. Well, what number’s between these too? It’s going to be six. So, therefore, we can say that if 𝐴 is the point four, 10 and 𝐵 is the point six, two, the midpoint of 𝐴𝐵 is going to be the second answer, five, six.

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