Question

find the distance between the two points in simplest radical form. answer attempt 1 out of 2

Explanation:

1. Explanation:

• First, assume the two - point formula for the distance \(d\) between two points \((x_1,y_1)\) and \((x_2,y_2)\) is \(d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\). But since the points are not given in coordinate form in the description, we need to assume some general steps. Let the two points be \((x_1,y_1)\) and \((x_2,y_2)\).
• Calculate the difference in \(x\) - coordinates: \(\Delta x=x_2 - x_1\).
• Calculate the difference in \(y\) - coordinates: \(\Delta y=y_2 - y_1\).
• Then square these differences: \((\Delta x)^2=(x_2 - x_1)^2\) and \((\Delta y)^2=(y_2 - y_1)^2\).
• Add the squared differences: \((x_2 - x_1)^2+(y_2 - y_1)^2\).
• Take the square - root of the sum to get the distance: \(d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\).
• However, since we don't have the actual coordinates of the two points from the image (the image is not clear enough to read the coordinates), let's assume the two points are \((x_1,y_1)\) and \((x_2,y_2)\) and go through the steps symbolically.
• Let's say we find the coordinates of the two points. For example, if the first point is \((x_1,y_1)\) and the second point is \((x_2,y_2)\).
• Step 1: Find the difference in \(x\) - coordinates
• Let \(a=x_2 - x_1\).
• Step 2: Find the difference in \(y\) - coordinates
• Let \(b=y_2 - y_1\).
• Step 3: Square the differences and sum them
• \(a^{2}+b^{2}=(x_2 - x_1)^2+(y_2 - y_1)^2\).
• Step 4: Take the square - root
• \(d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\).

1. Answer:

Since we don't have the actual coordinates of the two points from the image, we can't give a numerical answer. But the formula for the distance \(d\) between two points \((x_1,y_1)\) and \((x_2,y_2)\) in the coordinate - plane is \(d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\). If the points were \((x_1,y_1)\) and \((x_2,y_2)\), we would substitute the values into the formula to get the distance. For example, if the points were \((3, - 2)\) and \((6,1)\):

• \(x_1 = 3,y_1=-2,x_2 = 6,y_2 = 1\).
• \(x_2 - x_1=6 - 3=3\) and \(y_2 - y_1=1-(-2)=3\).
• \(d=\sqrt{(6 - 3)^2+(1 + 2)^2}=\sqrt{3^{2}+3^{2}}=\sqrt{9 + 9}=\sqrt{18}=3\sqrt{2}\).

If we assume the two points have coordinates \((x_1,y_1)\) and \((x_2,y_2)\), the general answer is \(d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\).

Answer:

1. Explanation:

• First, assume the two - point formula for the distance \(d\) between two points \((x_1,y_1)\) and \((x_2,y_2)\) is \(d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\). But since the points are not given in coordinate form in the description, we need to assume some general steps. Let the two points be \((x_1,y_1)\) and \((x_2,y_2)\).
• Calculate the difference in \(x\) - coordinates: \(\Delta x=x_2 - x_1\).
• Calculate the difference in \(y\) - coordinates: \(\Delta y=y_2 - y_1\).
• Then square these differences: \((\Delta x)^2=(x_2 - x_1)^2\) and \((\Delta y)^2=(y_2 - y_1)^2\).
• Add the squared differences: \((x_2 - x_1)^2+(y_2 - y_1)^2\).
• Take the square - root of the sum to get the distance: \(d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\).
• However, since we don't have the actual coordinates of the two points from the image (the image is not clear enough to read the coordinates), let's assume the two points are \((x_1,y_1)\) and \((x_2,y_2)\) and go through the steps symbolically.
• Let's say we find the coordinates of the two points. For example, if the first point is \((x_1,y_1)\) and the second point is \((x_2,y_2)\).
• Step 1: Find the difference in \(x\) - coordinates
• Let \(a=x_2 - x_1\).
• Step 2: Find the difference in \(y\) - coordinates
• Let \(b=y_2 - y_1\).
• Step 3: Square the differences and sum them
• \(a^{2}+b^{2}=(x_2 - x_1)^2+(y_2 - y_1)^2\).
• Step 4: Take the square - root
• \(d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\).

1. Answer:

Since we don't have the actual coordinates of the two points from the image, we can't give a numerical answer. But the formula for the distance \(d\) between two points \((x_1,y_1)\) and \((x_2,y_2)\) in the coordinate - plane is \(d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\). If the points were \((x_1,y_1)\) and \((x_2,y_2)\), we would substitute the values into the formula to get the distance. For example, if the points were \((3, - 2)\) and \((6,1)\):

• \(x_1 = 3,y_1=-2,x_2 = 6,y_2 = 1\).
• \(x_2 - x_1=6 - 3=3\) and \(y_2 - y_1=1-(-2)=3\).
• \(d=\sqrt{(6 - 3)^2+(1 + 2)^2}=\sqrt{3^{2}+3^{2}}=\sqrt{9 + 9}=\sqrt{18}=3\sqrt{2}\).

If we assume the two points have coordinates \((x_1,y_1)\) and \((x_2,y_2)\), the general answer is \(d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\).