Answer :
To calculate the distance between points A and B using Pythagoras' theorem, we need to find the lengths of the horizontal and vertical sides of the right triangle formed by points A and B.
The horizontal side (base) can be calculated as the difference between the x-coordinates of points A and B:
\[ \text{Base} = x_B - x_A = 9 - 2 = 7 \]
The vertical side (height) can be calculated as the difference between the y-coordinates of points A and B:
\[ \text{Height} = y_B - y_A = 7 - 1 = 6 \]
Now, we can use Pythagoras' theorem to find the hypotenuse (distance between points A and B):
\[ \text{Distance} = \sqrt{\text{Base}^2 + \text{Height}^2} \]
\[ \text{Distance} = \sqrt{7^2 + 6^2} \]
\[ \text{Distance} = \sqrt{49 + 36} \]
\[ \text{Distance} = \sqrt{85} \]
Now, calculating the square root of \(85\):
\[ \text{Distance} \approx 9.22 \text{ cm (1 d.p)} \]
So, the distance from point A to point B is approximately \(9.2\) centimeters.
The horizontal side (base) can be calculated as the difference between the x-coordinates of points A and B:
\[ \text{Base} = x_B - x_A = 9 - 2 = 7 \]
The vertical side (height) can be calculated as the difference between the y-coordinates of points A and B:
\[ \text{Height} = y_B - y_A = 7 - 1 = 6 \]
Now, we can use Pythagoras' theorem to find the hypotenuse (distance between points A and B):
\[ \text{Distance} = \sqrt{\text{Base}^2 + \text{Height}^2} \]
\[ \text{Distance} = \sqrt{7^2 + 6^2} \]
\[ \text{Distance} = \sqrt{49 + 36} \]
\[ \text{Distance} = \sqrt{85} \]
Now, calculating the square root of \(85\):
\[ \text{Distance} \approx 9.22 \text{ cm (1 d.p)} \]
So, the distance from point A to point B is approximately \(9.2\) centimeters.
