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Vsevolod [243]
3 years ago
7

Find the missing side length. Leave your answer in simplest radical form.

Mathematics
1 answer:
exis [7]3 years ago
6 0

Answer:

4√3

Step-by-step explanation:

For isosoles triangles the legs are congruent

v = u

--------------------

using the pythagorean theorem

(4√6)² = v² + v²

(16 * 6) = 2v²

Divide both sides by 2

16 * 3 = v²

Take the square root of both sides

4√3 = v

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Answer:

(a) A translation is a rigid transformation. How does this statement support line s being parallel to line r?

Because ALL of the points of line r move the same distance in the same direction, then the inclination of the line s doesn't change with respect line r.

(b) Write and expression for the slope of line r:

(k-n)/(j-m)

(c) Write and expression for the slope of line s:

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(d) Line q is a vertical is a vertical translation of line s 3 units down. P'' is the image of P'. What are the coordinates of P''?

The coordinates of P'' are:

P''=(m,n+ϴ-3)

Step-by-step explanation:

(a) A translation is a rigid transformation. How does this statement support line s being parallel to line r?

Because ALL of the points of line r move the same distance in the same direction, then the inclination of the line s doesn't change with respect line r.


(b) Write and expression for the slope of line r.

Line r goes through the points:

P=(m,n)=(xp,yp)→xp=m, yp=n

Q=(j,k)=(xq,yq)→xq=j, yq=k

Slope of line r is:

mr=(yq-yp)/(xq-xp)

Replacing the coordinates, the expression for the slope of line r is:

mr=(k-n)/(j-m)


(c) Write and expression for the slope of line s.

Line s goes through the points:

P'=(m,n+ϴ)=(xp',yp')→xp'=m, yp'=n+ϴ

Q'=(j,k+ϴ)=(xq',yq')→xq'=j, yq'=k+ϴ

Slope of line s is:

ms=(yq'-yp')/(xq'-xp')

Replacing the coordinates, the expression for the slope of line s is:

ms=[(k+ϴ)-(n+ϴ)]/(j-m)

Eliminating the parentheses in the numerator:

ms=[k+ϴ-n-ϴ]/(j-m)

Simplifyng:

ms=(k-n)/(j-m)


(d) Line q is a vertical is a vertical translation of line s 3 units down. P'' is the image of P'. What are the coordinates of P''?

3 units down, then change only the ordinate y:

P''=(xp',yp'-3)

Replacing xp' and yp':

P''=(m,n+ϴ-3)


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