Question

question
find the distance between the two points in simplest radical form.

Explanation:

1. Explanation:

• First, recall the distance - formula between two points \((x_1,y_1)\) and \((x_2,y_2)\) in a coordinate plane, which is \(d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\). However, since the points are not given explicitly in the question text, assume the two points are \((x_1,y_1)\) and \((x_2,y_2)\).
• Let's say we identify the coordinates of the two points from the graph. For example, if the first point is \((x_1,y_1)\) and the second point is \((x_2,y_2)\).
• Calculate the difference in the \(x\) - coordinates: \(\Delta x=x_2 - x_1\).
• Calculate the difference in the \(y\) - coordinates: \(\Delta y=y_2 - y_1\).
• Then square these differences: \((x_2 - x_1)^2\) and \((y_2 - y_1)^2\).
• 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 \(d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\).
• Simplify the radical if possible. For example, if \((x_2 - x_1)^2+(y_2 - y_1)^2 = a\times b^2\) (where \(a\) is not a perfect - square and \(b\) is an integer), then \(d = b\sqrt{a}\).

Since the points are not given numerically, we cannot perform specific calculations. But the general steps to find the distance between two points \((x_1,y_1)\) and \((x_2,y_2)\) are as above.
Since the points are not provided, we cannot give a numerical answer. If we assume the points are \((x_1,y_1)\) and \((x_2,y_2)\), the answer in terms of the distance formula is \(d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\). If we had specific points, for example, if the points were \((3,4)\) and \((6,8)\):

Step 1: Identify the coordinates

Let \((x_1,y_1)=(3,4)\) and \((x_2,y_2)=(6,8)\).

Step 2: Calculate \(\Delta x\) and \(\Delta y\)

\(\Delta x=x_2 - x_1=6 - 3 = 3\), \(\Delta y=y_2 - y_1=8 - 4 = 4\).

Step 3: Apply the distance formula

\(d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}=\sqrt{3^2 + 4^2}=\sqrt{9 + 16}=\sqrt{25}=5\).
But without the actual points from the graph, we can only state the formula.

Answer:

If the two points are \((x_1,y_1)\) and \((x_2,y_2)\), the distance \(d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\)