Question

1.1 Segment Length and Midpoint Find the distance between the two points: (7, 3) and (1, -5). ​

Answer 1

The distance between the points (7, 3) and (1, -5) is calculated using the distance formula, which involves subtracting and squaring the coordinates, and then taking the square root of the sum, resulting in a distance of 10 units.

Step-by-step explanation:

To find the distance between two points on the coordinate plane, we can use the distance formula derived from the Pythagorean theorem. The formula is:

Distance = \(\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}\)

For the points (7, 3) and (1, -5), we can plug these into the formula as follows:

1. Subtract the x-coordinates: 7 - 1 = 6
2. Subtract the y-coordinates: 3 - (-5) = 3 + 5 = 8
3. Square each difference: 6^2 = 36 and 8^2 = 64
4. Add the squares: 36 + 64 = 100
5. Take the square root of the sum: \(\sqrt{100}\) = 10

Therefore, the distance between the points (7, 3) and (1, -5) is 10 units.

Answer 2

10

Step-by-step explanation:

→ Find the difference in y - coordinates

-5 - 3 = -8

→ Find the difference in x coordinates

1 - 7 = -6

→ Use Pythagoras' theorem

√6² + 8² = 10