All categories

3 years ago

The image of the point (2, 1) under a translation is (-3, -2). Find

Mathematics

1 answer:

nirvana33 [79]3 years ago

8 0

Answer:

(-7, -12)

Explanation:

The translation of (2, 1) to (-3, -2) is 5 units left and 3 and 3 units down

2 - 5 = -3, x-coordinate = -3

1 - 3 = -2, y-coordinate = -2

Thus that makes the coordinates (-3, -2)

So that is taking away 5 from the x-axis and 3 away from the y-axis

-2 - 5 = -7, x-coordinate = -7

-9 - 3 = -12, y-coordinate = -12

Thus, the answer is (-7, -12)

You might be interested in

What is h ( t ) = − t ( 16 t + 7 ) in standard form PLEASE HELP !!!!

ExtremeBDS [4]

y = 2x - 4

y = 4x - 6

y = 3x - 4

that's what i got

6 0

3 years ago

Consider the parabola given by the equation: f(x) = 4x² - 6x - 8 Find the following for this parabola: A) The vertex: Preview B)

jeyben [28]

Answer:

The vertex: $(\frac{3}{4},-\frac{41}{4} )$

The vertical intercept is: $y=-8$

The coordinates of the two intercepts of the parabola are $(\frac{3+\sqrt{41} }{4} , 0)$ and $(\frac{3-\sqrt{41} }{4} , 0)$

Step-by-step explanation:

To find the vertex of the parabola $4x^2-6x-8$ you need to:

1. Find the coefficients a, b, and c of the parabola equation

$a=4, b=-6, \:and \:c=-8$

2. You can apply this formula to find x-coordinate of the vertex

$x=-\frac{b}{2a}$ , so

$x=-\frac{-6}{2\cdot 4}\\x=\frac{3}{4}$

3. To find the y-coordinate of the vertex you use the parabola equation and x-coordinate of the vertex ( $f(-\frac{b}{2a})=a(-\frac{b}{2a})^2+b(-\frac{b}{2a})+c$ )

$f(-\frac{b}{2a})=a(-\frac{b}{2a})^2+b(-\frac{b}{2a})+c\\f(\frac{3}{4})=4\cdot (\frac{3}{4})^2-6\cdot (\frac{3}{4})-8\\y=\frac{-41}{4}$

To find the vertical intercept you need to evaluate x = 0 into the parabola equation

$f(x)=4x^2-6x-8\\f(0)=4(0)^2-6\cdot 0-0\\f(0)=-8$

To find the coordinates of the two intercepts of the parabola you need to solve the parabola by completing the square

$\mathrm{Add\:}8\mathrm{\:to\:both\:sides}$

$x^2-6x-8+8=0+8$

$\mathrm{Simplify}$

$4x^2-6x=8$

$\mathrm{Divide\:both\:sides\:by\:}4$

$\frac{4x^2-6x}{4}=\frac{8}{4}\\x^2-\frac{3x}{2}=2$

$\mathrm{Write\:equation\:in\:the\:form:\:\:}x^2+2ax+a^2=\left(x+a\right)^2$

$x^2-\frac{3x}{2}+\left(-\frac{3}{4}\right)^2=2+\left(-\frac{3}{4}\right)^2\\x^2-\frac{3x}{2}+\left(-\frac{3}{4}\right)^2=\frac{41}{16}$

$\left(x-\frac{3}{4}\right)^2=\frac{41}{16}$

$\mathrm{For\:}f^2\left(x\right)=a\mathrm{\:the\:solutions\:are\:}f\left(x\right)=\sqrt{a},\:-\sqrt{a}$

$x_1=\frac{\sqrt{41}+3}{4},\:x_2=\frac{-\sqrt{41}+3}{4}$

4 0

3 years ago

Help with word problem!

creativ13 [48]

2 1/6 divided by 7/10

13/6 / 7/10 =

13/6 * 10/7 =

130/42 =

3 4/42. or 3 2/21 hours... three and two twenty-firsts

7 0

3 years ago

Look closely at the character of Alice in the film and the play versions of Alice’s Adventures in Wonderland. Does the character

Tems11 [23]

Answer:

In the movie, Tweedledee and Tweedledum and the talking flowers are incorporated into the original plot from Alice's Adventures in Wonderland. In the book, Alice eats little cakes in the White Rabbit's house to become smaller. In the movie, Alice eats carrots from The White Rabbit's garden to become smaller.

Step-by-step explanation:

3 0

2 years ago

HELP PLEASE ! if right will mark as brainliest !

bekas [8.4K]

Answer:

Step-by-step explanation:

so pay attentyion t the numbners

6 0

3 years ago