Put the steps in order to find the distance between these 2 points.
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1.Draw a right triangle by dropping a vertical side and a horizontal side.
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2.Determine the vertical side (2 units) and horizontal side (6 units) lengths by counting on the grid (be careful of the scale), or using the vertical coordinates (3 to 1) and horizontal coordinates (-2 to 4).
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3.4 + 36 = c^2
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4.
√40 is between √36 and √49, so between 6 and 7 - closer to 6, so about 6.3 units
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5.40 = c^2
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6.
√40 = √c^2
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7.Use the Pythagorean Theorem for right triangles to determine the diagonal length: 2^2 + 6^2 = c^2
the graph shows(-2,1) and a line going to (4,3)
To find the distance between the points (-2, 1) and (4, 3), you can follow these steps:
1. Draw a right triangle by dropping a vertical side and a horizontal side. In this case, draw a horizontal line segment from (-2, 1) to (4, 1) and a vertical line segment from (4, 1) to (4, 3).
2. Determine the lengths of the vertical and horizontal sides of the right triangle. You can do this by counting on the grid or using the coordinates. In this case, the vertical side is 2 units (from 1 to 3) and the horizontal side is 6 units (from -2 to 4).
3. Use the Pythagorean Theorem, which states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. So, you can write the equation as 2^2 + 6^2 = c^2, where c is the length of the hypotenuse (the distance between the two points).
4. Solve the equation: 4 + 36 = c^2. This simplifies to 40 = c^2.
5. To find the value of c, take the square root of both sides of the equation: √40 = √c^2, which gives you c ≈ √40.
6. Approximate the square root of 40. Since √40 is between √36 (which is 6) and √49 (which is 7), it will be closer to 6. So, the approximate value of √40 is about 6.3 units.
7. Therefore, the distance between the points (-2, 1) and (4, 3) is approximately 6.3 units.