Question Video: Finding the Distance between Two Given Points Using the Distance Formula | Nagwa Question Video: Finding the Distance between Two Given Points Using the Distance Formula | Nagwa

Question Video: Finding the Distance between Two Given Points Using the Distance Formula Mathematics • Sixth Year of Primary School

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Given points 𝐶(16, 20) and 𝐷(16, 10), calculate the distance between the two points, 𝐶 and 𝐷, considering that a length unit = 1 cm.

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Video Transcript

Given point 𝐶 16, 20 and 𝐷 16, 10, calculate the distance between the two points, 𝐶 and 𝐷, considering that a length unit equals one centimetre.

Well, what we can do to help us solve this problem is draw a little sketch to help us see what’s happening. So, we’ve been given two points, 𝐶 and 𝐷. Now, the first point is 𝐶, and its coordinates are 16, 20. So, this means 16 along the 𝑥-axis and 20 on the 𝑦-axis. And then, we’ve been given 𝐷. And 𝐷 has the coordinates 16, 10, so 16 on the 𝑥-axis and 10 on the 𝑦-axis.

And what we’re wanting to find is the length of 𝐶𝐷, which I’ve shown here cause I’ve drawn the line 𝐶𝐷. Now, because our 𝑥-coordinates are exactly the same, and we can see they’re both 16, it means that our line is a vertical line. So, we don’t have to deal with the horizontal component at all because, as we said, the 𝑥-coordinates are exactly the same. So therefore, the length of the line is gonna be the change in vertical coordinates, or the change in our 𝑦-coordinates.

So, we can see we’ve got 𝐶 has a coordinate 20 and 𝐷 has a coordinate 10. Therefore, the length 𝐶𝐷 is the distance between 𝐷 and 𝐶 in the vertical axis. So, the way that we can calculate this is by subtracting 10 from 20. And that’s because 20 is the greater value because that’s the 𝑦-coordinate of 𝐶. And then, we’re subtracting 10 because that’s the 𝑦-coordinate of 𝐷 away from it. And this gives the answer 10 units.

Well, is this the answer? Well, not quite, because the question wants us to find the distance between the two points. And the way you can do that is by using a little key we’ve been given. And that is that the length unit is equal to one centimetre. So therefore, we can say that the distance 𝐶𝐷 is gonna be equal to 10 centimetres. And that’s because we found that 𝐶𝐷 was equal to 10 units. 10 multiplied by one gives us 10, so the answer is 10 centimetres.

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