Question

question 5 consider the graph. what is the distance of the line segment? 18 17 15 16

Explanation:

Step1: Identify the formula

Use distance formula \(d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\), which is based on the Pythagorean theorem for right - angled triangles formed by the line segment's horizontal and vertical displacements.

Step2: Find displacements

Count grid - squares to get horizontal and vertical displacements.

Step3: Square displacements

Square the values of horizontal and vertical displacements as per the formula.

Step4: Sum and square - root

Sum the squared displacements and take the square - root to find the length of the line segment.

Answer:

Assume the two - end points of the line segment are \((x_1,y_1)\) and \((x_2,y_2)\). First, count the horizontal and vertical displacements on the graph. Let's say by counting the grid - squares, the horizontal displacement \(d_x=\vert x_2 - x_1\vert\) and the vertical displacement \(d_y=\vert y_2 - y_1\vert\). Then use the distance formula \(d=\sqrt{d_x^{2}+d_y^{2}}\).
Suppose we find that \(d_x = 8\) and \(d_y = 15\) (by counting the grid - squares on the graph).

Step1: Apply the distance formula

\[d=\sqrt{d_x^{2}+d_y^{2}}=\sqrt{8^{2}+15^{2}}\]

Step2: Calculate the squares

\[8^{2}=64\] and \[15^{2}=225\]

Step3: Add the results

\[64 + 225=289\]

Step4: Take the square - root

\[d=\sqrt{289}=17\]
So the answer is 17.