The learners I will be addressing are 9 th graders or students in Algebra 1. So in this question, it involved applying the Pythagorean theorem twice to find the distance between two different sets of points and then combining them using what we know about areas of rectangles. Now as before, we’ll start with a sketch. 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So the distance between the two points is . Now this generalised formula is useful because it gives us a formula that will always work and we can plug any numbers into it. (Derive means to arrive at by reasoning or manipulation of one or more mathematical statements.) And you may find it helpful to use that if you like to just substitute into a formula. Now units for this, well it’s an area. The surface of the Earth is curved, and the distance between degrees of longitude varies with latitude. using pythagorean theorem to find distance between two points The Pythagorean Theorem In a right triangle, the sum of the squares of the lengths of the legs is … So let’s look at the -coordinate first. The length of the vertical leg is 4 units. Now if I look at the vertical side of the triangle, well here the only thing that’s changing is the -coordinate. Now units for this, we haven’t been told that it’s a centimetre-square grid. So you’ll have seen before that the Pythagorean theorem can be extended into three dimensions. in Maths. And it’s changing from negative three to two. The -value changes from zero to four. If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked. So the length of that vertical line is gonna be the difference between those two -values. Locate the points (1, 3) and (-1, -1) on a coordinate plane. And I get - squared is equal to 45. So squared, the -coordinates, well the difference between those is it goes from two to three. Explain how you could use the Pythagorean Theorem to find the distance between the Step 1. So is equal to the square root of 45. Right, now I can write down what the Pythagorean theorem tells me in terms of and one, two, one, and two. And if you do that one way round, you will get for example a difference of five and square it to 25. The next step is to work out three squared, four squared, and one squared. 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