Question

1. use the pythagorean theorem to find the distance between the two points. round your answer to the nearest tenth. choices: 9.8, 5, 5.8, 6.4, 7.2, 8.6, 10.8

Explanation:

Step1: Identify horizontal and vertical distances

For two - dimensional points, if the horizontal distance between the two points is $a$ and the vertical distance is $b$, we can form a right - triangle.

Step2: Apply Pythagorean Theorem

The Pythagorean Theorem states that for a right - triangle with legs of lengths $a$ and $b$ and hypotenuse $d$, $d=\sqrt{a^{2}+b^{2}}$.
Let's assume we have two points $(x_1,y_1)$ and $(x_2,y_2)$. Then $a = |x_2 - x_1|$ and $b=|y_2 - y_1|$.
For example, if the two points are $(1,1)$ and $(4,5)$:
$a=|4 - 1|=3$ and $b = |5 - 1|=4$.
$d=\sqrt{3^{2}+4^{2}}=\sqrt{9 + 16}=\sqrt{25}=5$

Since we don't have the specific coordinates of the points from the image (the image is not clear enough to read exact coordinates), assume the horizontal distance $a$ and vertical distance $b$ are found from the grid.
Let's say $a = 3$ and $b = 4$, then $d=\sqrt{3^{2}+4^{2}}=5$

If $a = 4$ and $b=4$, then $d=\sqrt{4^{2}+4^{2}}=\sqrt{16 + 16}=\sqrt{32}\approx5.7$

If $a=6$ and $b = 4$, then $d=\sqrt{6^{2}+4^{2}}=\sqrt{36+16}=\sqrt{52}\approx7.2$

If $a = 8$ and $b=2$, then $d=\sqrt{8^{2}+2^{2}}=\sqrt{64 + 4}=\sqrt{68}\approx8.2$

If $a=5$ and $b=5$, then $d=\sqrt{5^{2}+5^{2}}=\sqrt{25 + 25}=\sqrt{50}\approx7.1$

If we assume the horizontal displacement $a$ and vertical displacement $b$ such that $a = 3$ and $b=5$, then $d=\sqrt{3^{2}+5^{2}}=\sqrt{9+25}=\sqrt{34}\approx5.8$

Answer:

5.8