Question

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: .

Answer 1

The slope of the line CD is 6 and the length of CD is √37.

Step-by-step explanation:

To find the slope (m) of the line CD, we can use the formula: m = (y2 - y1) / (x2 - x1)

Using the coordinates of points C(2, 2) and D(3, 8), we can calculate the slope:

m = (8 - 2) / (3 - 2) = 6 / 1 = 6

The length of CD can be found using the distance formula: √[(x2 - x1)^2 + (y2 - y1)^2]

Using the coordinates of points C(2, 2) and D(3, 8), we can calculate the length:

Length = √[(3 - 2)^2 + (8 - 2)^2] = √(1 + 36) = √37

Answer 2

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

=
`√((p-a)^2+(q-b)^2)`

AB=
`√((3-2)^2+(8-2)^2)=√(1+36)=√(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=
`(q-b)/(p-a)`

m=
`(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