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3 years ago

What is the distance between [(3 + 4i) + (2 - 3i)] and (9 - 2i)?

Mathematics

1 answer:

Semmy [17]3 years ago

5 0

Answer:

Step-by-step explanation:

(3 + 4i) + (2 - 3i) = 3 + 4i + 2 - 3i = 5 + i

distance between (5 + i) and (9 - 2i) is the difference between them. and difference means subtraction.

(9 - 2i) - (5 + i) = 9 - 2i - 5 - i = 4 - 3i

and since we are looking for a distance, we are looking for the absolute value of that subtraction.

after all, we could have done the subtraction also in the other direction

(5 + i) - (9 - 2i) = -4 + 3i

and this must be the same distance.

|(-4 + 3i)| = |(4 - 3i)|

and that is done by calculating the distance of any of these 2 points from (0,0) on the coordinate grid of complex numbers.

|(a +bi)| = sqrt(a² + b²)

in our case here

distance = sqrt(4² + (-3)²) = sqrt(16 + 9) = sqrt(25) = 5

as you can easily see, this is (as expected) the same for the result of the subtraction in the other direction :

sqrt((-4)² + 3²) = sqrt(16+9) = sqrt(25) = 5

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Given segments AB and CD intersect at E.

nata0808 [166]

The length of a segment is the distance between its endpoints.

$\mathbf{AB = 3\sqrt{2}}$
AB and CD are not congruent
AB does not bisect CD
CD does not bisect AB

(a) Length of AB

We have:

$\mathbf{A = (1,2)}$

$\mathbf{B = (4,5)}$

The length of AB is calculated using the following distance formula

$\mathbf{AB = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}}$

So, we have:

$\mathbf{AB = \sqrt{(1 - 4)^2 + (2 - 5)^2}}$

$\mathbf{AB = \sqrt{18}}$

Simplify

$\mathbf{AB = 3\sqrt{2}}$

(b) Are AB and CD congruent

First, we calculate the length of CD using:

$\mathbf{CD = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}}$

Where:

$\mathbf{C = (2, 4)}$

$\mathbf{D = (2, 1)}$

So, we have:

$\mathbf{CD = \sqrt{(2 -2)^2 + (4 - 1)^2}}$

$\mathbf{CD = \sqrt{9}}$

$\mathbf{CD = 3}$

By comparison

$\mathbf{CD \ne AB}$

Hence, AB and CD are not congruent

(c) AB bisects CD or not?

If AB bisects CD, then:

$\mathbf{AB = \frac 12 \times CD}$

The above equation is not true, because:

$\mathbf{3\sqrt 2 \ne \frac 12 \times 3}$

Hence, AB does not bisect CD

(d) CD bisects AB or not?

If CD bisects AB, then:

$\mathbf{CD = \frac 12 \times AB}$

The above equation is not true, because:

$\mathbf{3 \ne \frac 12 \times 3\sqrt 2}$

Hence, CD does not bisect AB

Read more about lengths and bisections at:

brainly.com/question/20837270

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3 years ago

True or false.The perimeter is the boundary of a shape or an object.

vredina [299]

Answer:

I got this off the internet : In geometry, perimeter can be defined as the path or the boundary that surrounds a shape. It can also be defined as the length of the outline of a shape.

Step-by-step explanation:

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2 years ago

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Please find the surface area

nevsk [136]

4*(10*12/2)+4*(12*9)+(12*12)= 816 ft^2

the surface area is 816 ft^2.

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3 years ago

Find the solutions to the equation by completing the square. x2-6x=7

lianna [129]

Subtract 7 from both sides

x^2 - 6x - 7 = 7 - 7

Simplify

x^2 - 6x - 7 = 0

Answer :

The final solutions to the quadratic equation are:

x = 7, -1

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3 years ago

Find the slope of the line that is perpendicular to the line that passes through the points (5,2) and (8,1)

Naya [18.7K]

Answer:

Step-by-step explanation:

The slope of the line passing through the points is

m = (y2-y1)/(x2-x1)

= ( 1-2)/(8-5)

= -1/3

The slope that is perpendicular is the negative reciprocal which is

- ( 1/(-1/3)

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3 years ago