Question

Pls include explanation

Answer 1

Answer:

• See below

Step-by-step explanation:

Corresponding sides have equal ratios:

• OB / OP = OK / OS

Let the y-coordinate of the point K is y, then we have:

• 5 / 8 = y / - 12
• y = - 12*5/8
• y = - 7.5

Note, taken the coordinates of end points not the absolute distance.

The coordinates of the point K are (0, - 7.5)

The scale factor is:

• k = OP / OB = 8/5 = 1.6 or
• k = OS / OK = -12 / -7.5 = 1.6

Answer 2

Answer:

K = (0, -7.5)

Scale factor = 1.6

Step-by-step explanation:

If ΔBOK is similar to ΔPOS then the ratios of their corresponding sides are the same.

Given side lengths:

• OP = 8 units
• OB = 5 units
• OS = 12 units

Therefore:

$\sf \implies OP:OS = OB:OK$

$\sf \implies 8:5= 12:OK$

$\implies \sf \dfrac{8}{5}=\dfrac{12}{OK}$

$\implies \sf 8 \cdot OK = 12 \cdot 5$

$\implies \sf OK=\dfrac{60}{8}$

$\implies \sf OK=7.5$

Therefore, the coordinates of K are (0, -7.5).

To find the scale factor, simply divide the corresponding side lengths of the larger triangle by the smaller triangle:

$\implies \sf scale\:factor=\dfrac{OP}{OB}=\dfrac{8}{5}=1.6$

Learn more about similar triangles here:

https://brainly.com/question/21427237

https://brainly.com/question/27928866