Consider the following pair of points.

Mathematics

1 answer:

dedylja [7]3 years ago

4 0

Answer:

The answer is

<h2> $\sqrt{265} \: \: or \: \: 16.28 \: \: \: \: units$ </h2>

Step-by-step explanation:

The distance between two points can be found by using the formula

where

(x1 , y1) and (x2 , y2) are the points

From the question the points are

(9,-8) and (-7,-5)

The distance between them is

$d = \sqrt{ ({9 + 7})^{2} + ({ - 8 + 5})^{2} } \\ = \sqrt{ {16}^{2} + ( { - 3})^{2} } \\ = \sqrt{256 + 9} \: \: \: \: \: \: \: \: \: \\ = \sqrt{265} \: \: \: \: \: \: \\ = 16.27882$

We have the final answer as

$\sqrt{265} \: \: or \: \: 16.28 \: \: \: \: units$

Hope this helps you

You might be interested in

A submarine travels 6.6 km due West from its base and then turns and travels due South for 3.9

geniusboy [140]

Answer:

$7.7$ km

Step-by-step explanation:

The submarine's path from its base forms a right triangle when its final position is "connected" to the base. We know that the right triangle has legs of $6.6$ km and $3.9$ km, and we need to find the length of its hypotenuse. To do so, we can use the Pythagorean Theorem, which states that in a right triangle, $a^{2}+b^{2} =c^{2}$ , where $a$ and $b$ are the lengths of the triangle's legs and $c$ is the length of the triangle's hypotenuse. In this case, we know what $a$ and $b$ are, and we need to solve for c, so after substituting the given values of $a$ and $b$ into $a^{2}+b^{2} =c^{2}$ to solve for c, we get:

$a^{2}+b^{2} =c^{2}$

$6.6^{2} +3.9^{2} =c^{2}$ (Substitute $a=6.6$ and $b=3.9$ into the equation)

$43.56+15.21=c^{2}$ (Evaluate the squares on the LHS)

$58.77=c^{2}$ (Simplify the LHS)

$c^{2}=58.77$ (Symmetric Property of Equality)

$\sqrt{c^{2} } =\sqrt{58.77}$ (Take the square root of both sides of the equation)

$c=7.7,c=-7.7$ (Simplify)

$c=-7.7$ is an extraneous solution because you can't have negative distance, if that makes sense, so therefore, the submarine is approximately $7.7$ km away from its base. Hope this helps!