The equation to derive the distance d is $\sqrt{(x2-x1)^2+(y2-y1)^2}$ . The lengths of the other legs of the given triangle are (y2 - y1) and (x2 - x1).

<h3>What is the formula for calculating the distance between two points?</h3>

Consider the two points (x1, y1) and (x2, y2)

The formula used for calculating the distance between the two points is

distance = $\sqrt{(x2-x1)^2+(y2-y1)^2}$

<h3>Calculation:</h3>

Given that,

The triangle in the graph has vertices (x1, y1), (x2, y2), and (x2, y1)

Since this triangle makes 90°, it is a right-angled triangle.

Hypotenuse = (x1, y1) to (x2, y2), Adjacent = (x1, y1) to (x2,y1), and Opposite = (x2, y1) to (x2, y2).

Consider the length of the hypotenuse = d

So, using the distance formula, the length of the hypotenuse(d) is,

$d = \sqrt{(x2-x1)^2+(y2-y1)^2}$

And the lengths of the other two legs of the given triangle are,

Length of the adjacent side: (x1, y1) to (x2,y1)

= $\sqrt{(x2-x1)^2+(y1-y1)^2}$

= $\sqrt{(x2-x1)^2+0}$

= $(x2-x1)$

Length of the opposite side: (x2, y1) to (x2, y2)

= $\sqrt{(x2-x2)^2+(y2-y1)^2}$

= $\sqrt{0+(y2-y1)^2}$

= $(y2-y1)$

Therefore, the derived distances for the given triangle are:

$d=\sqrt{(x2-x1)^2+(y2-y1)^2}$ , (x2 - x1), and (y2 - y1).

Learn more about the distance between two points here:

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4 0

1 year ago

Jamie evaluated this expression. StartFraction left-bracket (2 cubed) (2) right-bracket Superscript 4 Baseline Over 2 Superscrip

SVETLANKA909090 [29]

Answer:

Step-by-step explanation:

Given the expression

$\frac{(2^3)(2)^4}{2^{10}} \\$

Using the following laws of indices;

$\frac{a^m}{a^n} = a^{m-n}\\a^m \times a^n = a^{m+n}$

The expression becomes;

Step 1: Multiplication rule

$=\frac{(2^3)(2)^4}{2^{10}} \\= \frac{2^{3+4}}{2^{10}}\\= \frac{2^7}{2^{10}}$

Using the division rule of exponent (Quotient of powers);

$= \frac{2^7}{2^{10}} \\= 2^{7-10}\\= 2^{-3}\\also \ a^{-m} = \frac{1}{a^m}\\ 2^{-3}= \frac{1}{2^3}\\\frac{1}{2^3} = \frac{1}{8}$

Hence the result of the expression is 1/8

5 0

3 years ago

Read 2 more answers

ThEre Is a hiddEn message within this question. If you can DIscover It, you wIll Have completed the 1st step of this puzzle. Aft

ladessa [460]

Answer:

Eiediiih

Step-by-step explanation:

That’s what the capital letters spell

3 0

2 years ago