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dezoksy [38]
3 years ago
14

Line Segment BC has endpoints B (3,5) and C (7,15). Find the missing coordinates of A (x,9) and D (17,y) such that AB and CD are

perpendicular to BC.
Mathematics
1 answer:
o-na [289]3 years ago
4 0

Answer:

<em>x=-7</em>

<em>y=11</em>

Step-by-step explanation:

<u>Perpendicular Vectors</u>

Two vectors defined as their endpoints \vec u= and \vec v= are perpendicular if their dot product a.b is zero. The dot product is

\vec u.\vec v=ac+bd

In other words

ac+bd=0

Let's treat all the points as the extremes of vectors, so we can easily find the missing coordinates

B (3,5) and C (7,15) define a segment, the vector  

\overrightarrow{BC}==

The point A is A (x,9), we need to form a vector with B

\overrightarrow{AB}==

this vector must be perpendicular to BC, so, applying the dot product we have

4(x-3)+40=0

4x-12=-40

x=-7

The point D is D(17,y), we need to form a vector with C

\overrightarrow{CD}==

this vector must be perpendicular to BC, so, applying the dot product we have

(4)(10)+(10)(y-15)=0

40+10y-150=0

10y=110

y=11

The points are

\boxed{A(-7,9), D(17,11)}

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Quadrilateral ABCD is a rectangle. If AE = 36 and CE = 2x - 4, find x.<br> B<br> E<br> А.<br> D
krek1111 [17]

The value of the x is 20 if the quadrilateral ABCD is a rectangle and  AE = 36 and CE = 2x - 4 because the diagonal of the rectangle bisect each other.

<h3>What is the area of the rectangle?</h3>

It is defined as the space occupied by the rectangle, which is planner 2-dimensional geometry.

The formula for finding the area of a rectangle is given by:

Area of rectangle = length × width

We know that the diagonal of the rectangle bisect each other.

AE = CE

36 = 2x - 4

2x = 40

x = 20

Thus, the value of the x is 20 if the quadrilateral ABCD is a rectangle and  AE = 36 and CE = 2x - 4 because the diagonal of the rectangle bisect each other.

Learn more about the rectangle here:

brainly.com/question/15019502

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2 years ago
What is the value of 948 x 10²?<br><br>A. 9.58<br>B. 95.8<br>C. 9,580<br>D. 95,800​
Rasek [7]
The answer is 94800
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3 years ago
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Solve the equation.<br><br> −10x + 1 + 7x = 37
matrenka [14]
You combine like terms which are -10x and 7x and 1 and 37. Then it becomes -3x=36. x would equal to 36/-3, which is -12.
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What is the product of (3x+7) and (x-7) ?
sleet_krkn [62]

Answer: The product of (3x+7) and (x-7) equals 3x^2 + 28x + 49

Step-by-step explanation:

To find the product of (3x+7) and (x-7) means to multiply both variables: To multiply both variables, we first multiply 3x by the expression, x - 7, then multiply 7 by the expression, x - 7.

(3x × x) +( 3x × 7) + (7 × x) + ( 7 × 7)

= 3x^2 + 21x + 7x + 49

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4 0
3 years ago
Pls help me for brainliest answer
Oksana_A [137]

Answer:

1.17 euros

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please mark as brainliest

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