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Gennadij [26K]
3 years ago
15

The endpoints of are A(2, 2) and B(3, 8). is dilated by a scale factor of 3.5 with the origin as the center of dilation to give

image . What are the slope (m) and length of ? Use the distance formula to help you decide: .
Mathematics
2 answers:
goldfiish [28.3K]3 years ago
6 0

Answer:

The given line segment whose end points are A(2,2) and B(3,8).

Distance AB is given by distance formula , which is

if we have to find distance between two points (a,b) and (p,q) is

=  \sqrt{(p-a)^2+(q-b)^2}

AB= \sqrt{(3-2)^2+(8-2)^2}=\sqrt{1+36}=\sqrt{37} = 6.08 (approx)

Line segment AB is dilated by a factor of 3.5 to get New line segment CD.

Coordinate of C = (3.5 ×2, 3.5×2)= (7,7)

Coordinate of D = (3.5×3, 3.5×8)=(10.5,28)

CD = AB × 3.5

CD = √37× 3.5

     = 6.08 × 3.5

= 21.28 unit(approx)

2. Slope of line joining two points (p,q) and (a,b) is given by

m=\frac{q-b}{p-a}

m= \frac{8-2}{3-2}=6

As the two lines are coincident , so their slopes are equal.

Slope of line AB=Slope of line CD = 6




Alla [95]3 years ago
6 0
The slopes of both are:m=\frac{y2-y1}{x2-x1}= \frac{8-2}{3-2}=  \frac{6}{1}=6
Length of AB (using the distance formula):AB=\sqrt{(3-2)^{2} +(8-2) ^{2} } = \sqrt{1+36} = \sqrt{37}=6.082
Length of the image: 3.5 * 6.082 = 21.287
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