Mathematics, 22.09.2019 03:30 ughh13

Segment
ab
is the hypotenuse of the right isosceles δabc with a(–6, –2) and b(–6, 5). find all possible coordinates of c.

Answers: 3

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Answer from: safi30360oz0c34

The possible first coordinates of point C are (-2.5,1.5)

The possible second coordinates of point C are (-9.5,1.5)

Step-by-step explanation:

we know that

Triangle ABC is a right isosceles triangle

Is a 45°-90°-45° triangle

AC=BC

we have

A(-6,-2), B(-6,5)

step 1

Find the length side of the hypotenuse AB

$AB=5-(-2)=7\ units$

step 2

Applying the Pythagoras Theorem

Find the length side of leg AC

$AB^{2}=AC^{2}+BC^{2}$

Remember that

AC=BC

substitute the given values

$7^{2}=AC^{2}+AC^{2}$

$49=2AC^{2}$

$AC^{2}=\frac{49}{2}$

$AC=\frac{7\sqrt{2}}{2}\ units$

step 3

Find the first possible coordinates of C

The point C is located at right of point A

Determine the x-coordinate of point C

The x-coordinate of point C must be equal to the x-coordinate of point A plus the horizontal distance between point A and point C

Let

ACx ------> the horizontal distance between point A and point C

The horizontal distance between point A and point C is equal to the distance AC multiplied by cos(45)

$ACx=(AC)cos(45\°)$

we have

$cos(45\°)=\frac{\sqrt{2}}{2}$

$AC=\frac{7\sqrt{2}}{2}\ units$

substitute

$ACx=(\frac{7\sqrt{2}}{2})\frac{\sqrt{2}}{2}=3.5\ units$

The x-coordinate of point C is

Cx=-6+3.5=-2.5

Determine the y-coordinate of point C

The y-coordinate of point C must be equal to the y-coordinate of point A plus the vertical distance between point A and point C

Let

ACy ------> the vertical distance between point A and point C

The vertical distance between point A and point C is equal to the distance AC multiplied by sin(45)

$ACy=(AC)sin(45\°)$

we have

$sin(45\°)=\frac{\sqrt{2}}{2}$

$AC=\frac{7\sqrt{2}}{2}\ units$

substitute

$ACy=(\frac{7\sqrt{2}}{2})\frac{\sqrt{2}}{2}=3.5\ units$

The y-coordinate of point C is

Cy=-2+3.5=1.5

therefore

The possible first coordinates of point C are (-2.5,1.5)

step 4

Find the second possible coordinate of C

The point C is located at left of point A

Determine the x-coordinate of point C

The x-coordinate of point C must be equal to the x-coordinate of point A minus the horizontal distance between point A and point C

Let

ACx ------> the horizontal distance between point A and point C

The horizontal distance between point A and point C is equal to the distance AC multiplied by cos(45)

$ACx=(AC)cos(45\°)$

we have

$cos(45\°)=\frac{\sqrt{2}}{2}$

$AC=\frac{7\sqrt{2}}{2}\ units$

substitute

$ACx=(\frac{7\sqrt{2}}{2})\frac{\sqrt{2}}{2}=3.5\ units$

The x-coordinate of point C is

Cx=-6-3.5=-9.5

Determine the y-coordinate of point C

The y-coordinate of point C must be equal to the y-coordinate of point A plus the vertical distance between point A and point C

Let

ACy ------> the vertical distance between point A and point C

The vertical distance between point A and point C is equal to the distance AC multiplied by sin(45)

$ACy=(AC)sin(45\°)$

we have

$sin(45\°)=\frac{\sqrt{2}}{2}$

$AC=\frac{7\sqrt{2}}{2}\ units$

substitute

$ACy=(\frac{7\sqrt{2}}{2})\frac{\sqrt{2}}{2}=3.5\ units$

The y-coordinate of point C is

Cy=-2+3.5=1.5

therefore

The possible second coordinates of point C are (-9.5,1.5)

see the attached figure to better understand the problem

Segment ab is the hypotenuse of the right isosceles δabc with a(–6, –2) and b(–6, 5). find all poss

Answer from: Quest

2500

step-by-step explanation:

Answer from: Quest

step-by-step explanation:

if you want to solve percent error follow these steps.

1. subtract the accepted value from the experimental value.

2. take the absolute value of step 1.

3. divide that answer by the accepted value.

4. multiply that answer by 100 and add the % symbol to express the answer as a percentage.

if you want to solve percent of change just do this.

1. work out the difference (increase) between the two numbers you are comparing.

2. divide the increase by the original number and multiply the answer by 100. if your answer is a negative number then this is a percentage decrease.

hope this : )

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