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3 years ago

Huy rotated the figure 90 degrees counterclockwise about the origin. What are the new coordinates of point C?

Mathematics

1 answer:

lubasha [3.4K]3 years ago

6 0

Step-by-step explanation:

90° counterclockwise = 270° clockwise

Algebraic Representation : 270° clockwise turn,

( x , y ) ==> ( y , - x )

C ( 5 , 1 ) ==> C' ( 1 , - 5 )

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Two objects are moving along separate linear paths where each path is described by position, d, and time, t. The variable d is m

Leni [432]

Answer:

it would start at 2.2 on the y axis and go up 2.5 and over 1

Step-by-step explanation:

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3 years ago

Can someone PLEASE explain in simple terms which trigonometric ratio to use, like tangent, cosine, or sine, and WHY?

natulia [17]

Answer:

Use law of Cosines or Tangent

Step-by-step explanation:

This is a SAS triangle, where you have have an angle adjacent to two side lengths. But given that it is a right triangle, you can find the hypotenuse by just using the tangent formula. You can find the quantity of any angle by applying tan= opposite side/adjacent side length.

However, lets say you want to find the opposite side, side XZ, you can use the law of cosine which basically states:

c=a^2+b^2﹣2abcos(angle number). But since it is a right triangle, just use the hypotenuse theorem which states: C^2 = A^2 + B^2

The answer for XZ would thus be: squareroot of 136 or 2(34)^1/2.

Hope this helps :)

7 0

3 years ago

What are the coordinates of the orthocenter of △JKL with vertices at J(−4, −1) , K(−4, 8) , and L(2, 8) ?

PilotLPTM [1.2K]

ANSWER

The orthocenter is $(-4,8)$

EXPLANATION

The orthocenter is the point of intersection of all the altitudes of a triangle.

If it is a right angle triangle then the orthocenter is the point at which the right angle is made.

If it is not a right angle triangle, then you have to find the equations of any two of the altitudes and solve simultaneously.

So you must first check to see if it is a right angle triangle that way you do not have to do bunch work.

The given triangle has vertices $J(-4,-1)$ , $(-4,8)$ , and $L(2,8)$ .

$Slope_{JK}=\frac{8--1}{-4--4}$

$Slope_{JK}=\frac{8+1}{-4+4}$

$Slope_{JK}=\frac{9}{0}$

Since the denominator is zero, the slope is undefined.

If the slope of a straight line is undefined, then that line is parallel to the y-axis. In other words, it is a vertical line.

$Slope_{JL}=\frac{8--1}{2--4}$

$Slope_{JL}=\frac{8+1}{2+4}$

$Slope_{JL}=\frac{9}{6}$

$Slope_{JL}=\frac{3}{2}$

$Slope_{KL}=\frac{8-8}{2--4}$

$Slope_{KL}=\frac{0}{2+4}$

$Slope_{KL}=\frac{0}{6}$

$Slope_{KL}=0$

if a straight line has a slope of zero, that line is parallel to the x-axis or it is horizontal.

From the slopes we can see that side KL of the triangle is horizontal and side JK is vertical. This two sides will meet at right angles at K.

See graph.

Therefore the coordinates of K, $(-4,8)$ is the orthocenter of the given triangle.

3 0

3 years ago

2y+7 ÷ -4y - 10 Evaluate the expression below when y = -3

Nina [5.8K]

2y+7÷-4y-10
2(-3)+7÷-4(-3)-10
-6+7÷12-10
$\frac{7}{12}$ -6-10
$\frac{7}{12} -16
= \frac{7}{12} - \frac{192}{12} 
=- \frac{185}{12} 
=-15 \frac{5}{12}$

7 0

3 years ago

The sum of 3 and a number is between -2 and 17.

kumpel [21]

Answer:

The number, x = { -5 < x < 14}

This means x is any integer between -5 and 14

Step-by-step explanation:

From the statement, let the number be x

3 + x = y; y = { -2 < y < 17}

This means that y is any integer between -2 and 17

Therefore, x = y - 3

Subtract 3 from the limits of y

i.e. -2 - 3 = -5 and 17 - 3 = 14

Hence, x = { -5 < x < 14}

4 0

3 years ago