Item 11 Which points divide overline AB into segments with lengths in the ratios 1:3 or 3:1?

(9, 2)

Step-by-step explanation:

What point divides the directed line segment ​ AB¯¯¯¯¯ ​ ⁢ into a 3:1 ratio?

coordinate plane with segment A B with A at (0, 2) and B at (12, 2)

(3, 2)

(4, 2)

(8, 2)

(9, 2)

Solution:

If point O(x, y) divides the line segment AB with endpoints A() and B() in the ratio n:m, the coordinates of O is:

Let us assume C(x, y) is the point that divides  segment A B with A at (0, 2) and B at (12, 2) in the ratio 3 : 1. Hence:

Therefore the coordinate of point C is at (9, 2).

the length of o'p' is .

step-by-step explanation:

it is given that the quadrilateral m'n'o'p' is the image of quadrilateral mnop after dilation.

the center of dilation is origin and the scale factor is 1.5.

in dilation the image and preimge are similar figures. it means the sides of image and preimage are proportional.

the scale factor is defined as

the scale factor is 1.5.

multiply both sides by op.

note: if the value of op is given, then multiply the value of op with 1.5 to get the length of side o'p'.

therefore length of o'p' is .

dilation scale factor 2: starting with δabc, draw the dilation image of the triangle with a center at the origin and a scale factor of two. notice that every coordinate of the original triangle has been multiplied by the scale factor (x2). dilation with scale factor 2, multiply by 2.