triangle ABC has vertices A (0,2), B (4,4), and C (-1,4). what are the vertices of its image with a scale factor of 4?

What is the equation, in point-slope form, of the line that is perpendicular to the given line and passes through the

Svetradugi [14.3K]

keeping in mind that perpendicular lines have negative reciprocal slopes, hmmmm what's the slope of that line above anyway,

$\bf (\stackrel{x_1}{1}~,~\stackrel{y_1}{-1})\qquad (\stackrel{x_2}{4}~,~\stackrel{y_2}{2}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{2}-\stackrel{y1}{(-1)}}}{\underset{run} {\underset{x_2}{4}-\underset{x_1}{1}}}\implies \cfrac{2+1}{3}\implies 1 \\\\[-0.35em] ~\dotfill$

$\bf \stackrel{\textit{perpendicular lines have \underline{negative reciprocal} slopes}} {\stackrel{slope}{\underline{1}\implies \cfrac{\underline{1}}{1}}\qquad \qquad \qquad \stackrel{reciprocal}{\cfrac{1}{\underline{1}}}\qquad \stackrel{negative~reciprocal}{-\cfrac{1}{\underline{1}}\implies -1}}$

so we're really looking for the equation of a line whose slope is -1 and runs through (2,5)

$\bf (\stackrel{x_1}{2}~,~\stackrel{y_1}{5})~\hspace{10em} \stackrel{slope}{m}\implies -1 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{5}=\stackrel{m}{-1}(x-\stackrel{x_1}{2}) \\\\\\ y-5=-x+2\implies y=-x+7$

8 0

3 years ago

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Maya is learning to drive, so this weekend she practiced driving 1/2 of a mile with her mother and another 3/4 of a mile with he

vitfil [10]

Step-by-step explanation:

1/2 + 3/4

= 2/4 + 3/4

= 5/4

= 1 and 1/4 miles

6 0

3 years ago

NEED HELP Fast open up the Screenshot

Evgesh-ka [11]

I think the answer is A but I am not sure. I think you would take the opposite of the y axis.

8 0

3 years ago

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I need help with this question. can someone please help me

Ahat [919]

-2x + y =3
use 5 number and put it in above equation to find y, I will use -2,-1,0,1,2
x y
-2 -1
-1 1
0 3
1 5
2 7

Then draw the graph, find another point in the graph which intersect the slope,
lets say i found (-3,-3)which is on the slope
to prove it, i put (-3,-3) in the equation -2x + y = 3
and i got
3 = 3
Thus it is correct.

7 0

3 years ago

Trigonometry:

Trava [24]

A. The approximate height of the building is 100 m

B. We can use the arc length formula to obtain an approximation of BC since angle A is small.

A.

The approximate height of the building is 100 m

To find the approximate height of the building, we consider the diagram.

From the diagram, we have that using trigonometry,

tanA = BC/AB

Now

A = 0.05 radians,
BC = height of building and
AB = 2 km = 2000 m

<h3 /><h3>Finding the value of BC</h3>

So, making BC subject of the formua, we have

BC = ABtanA

Substituting the values of the variables into the equation, we have

BC = ABtanA

BC =2000tan0.05

BC = 2000 × 0.05

BC = 100 m

So, the approximate height of the building is 100 m

B.

We can use the arc length formula to obtain an approximation of BC since angle A is small.

<h3 /><h3>Arc Length Formula</h3>

We know that the arc length formula L = rФ where

r = radius and
Ф = angle in radians

<h3 /><h3>The approximate height</h3>

Now BC = ABtanA

We know that Ф ≅ tanФ when Ф is small.

<h3 /><h3>The comparison</h3>

So, BC = AB × A which is the arc length formula with

L = BC,
r = AB and
Ф = A

So, we can use the arc length formula to obtain an approximation of BC since angle A is small.

Learn more about approximate height of building here:

brainly.com/question/3144976

7 0

2 years ago