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liraira [26]
3 years ago
5

Using properties of parallelograms, RSTU is a parallelogram that has vertices R (-3,1), S (3,4), and T( 6,2(. What are the coord

inates of point U.

Mathematics
1 answer:
ElenaW [278]3 years ago
8 0

Answer:

(0, -1)

Step-by-step explanation:

A parallelogram is a quadrilateral (has four sides) in which opposite sides are parallel to each other. Also for a parallelogram, the opposite sides and angles are equal to each other.

Hence for parallelogram RSTU, RS // TU and RU // ST

Let the coordinate of U be (x , y). Two lines are parallel to each other if their slopes are equal, hence:

Slope of RS = (4 - 1) /[3 - (-3)] = 3/6 = 0.5

Slope of ST = (2 - 4) /[6 - 3] = -2/3

Slope of RU = (y - 1) /[x - (-3)] = (y - 1) / (x + 3)

Slope of TU = (y - 2) /[x - 6]

Slope of RU = Slope of ST

(y - 1) / (x + 3) = -2/3

3y - 3 = -2x -6

2x + 3y = -6 + 3

2x + 3y = -3                  (1)

Slope of RS = Slope of TU

0.5 = (y - 2) /[x - 6]

0.5x - 3 = y  - 2

0.5x - y = 1                  (2)

Solving 1 and 2 simultaneously gives:

x = 0, y = -1

Therefore the coordinates of U = (0, -1)

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Tamiku [17]

\qquad \qquad  \bf \huge\star \:  \:  \large{  \underline{Answer} }  \huge \:  \: \star

\qquad❖ \:  \sf   \: \angle C  = 63 \degree

\textsf{  \underline{\underline{Steps to solve the problem} }:}

\qquad❖ \:  \sf \:x + 4x  + 12 + x=180°

( Angle EBA= Angle DBC, and the three angles sum upto 180° due to linear pair property )

\qquad❖ \:  \sf \:6x + 12 = 180

\qquad❖ \:  \sf \:6x = 180 - 12

\qquad❖ \:  \sf \:6x = 168

\qquad❖ \:  \sf \:x = 28 \degree

Next,

\qquad❖ \:  \sf   \: \angle C + \angle D + x = 180°

\qquad❖ \:  \sf   \: \angle C +3x + 5  + x = 180°

\qquad❖ \:  \sf   \: \angle C +4x  = 180 - 5

\qquad❖ \:  \sf   \: \angle C +4(28)  = 175

( x = 28° )

\qquad❖ \:  \sf   \: \angle C +112  = 175

\qquad❖ \:  \sf   \: \angle C  = 175 - 112

\qquad❖ \:  \sf   \: \angle C  = 63 \degree

\qquad \large \sf {Conclusion}  :

\qquad❖ \:  \sf   \: \angle C  = 63 \degree

4 0
1 year ago
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Svet_ta [14]

Answer:

2(5)+5=15

Step-by-step explanation:

1. you have the equation 2b+c

2. then you add the numbers for c and b

3. so b=5 and c=5

4. once you add it into the problem then you get 2(5)+5 make sure you remember to times 2 x 5

5. then you do PEMDAS

6. you do multiply so 2x5 is 10

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barxatty [35]
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Steps for Solving :

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15•4 (to get 40%)
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yawa3891 [41]

Answer:

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Step-by-step explanation:

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Explanation:

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