Geometry give g(1,2) and k(8,12). find the coordinates of p that partitions gk in the ratio of 3: 2

A point P on the line segment GK may be parametrically represented as

t is a real parameter which controls where on the segment P is.  t=0 means P=G, t=1 means P=K.  We're interested in the t that gives a 3:2 ratio for PG:PK.  That's closer to K so t>1/2.   t=3/(3+2) = 3/5.

(26/5, 8)

(5.2, 8)

Step-by-step explanation:

Given : G(1,2) and K (8,12).

To find :  The coordinates of P that partitions gk in the ratio of 3:2

Section formula :

The line segment having endpoints (a,b) and (c,d) is divided in ration m:n by point M , then the coordinates of the M will be :-

Similarly,

Now simplify , we get

x=5.2  and y=8

Hence, the coordinates of P that partitions GK in the ratio of 3:2 = (5.2, 8)

x + y = 90 5x – 10y = 90 90 – 10y = 5x 90 + 10y = 5x

step-by-step explanation:

last month maria hiked the 5-mile mountain trail a number of times and she hiked the 10-mile canal trail several times. let x represent the number of times she hiked the 5-mile trail, and let y represent the number of times she hiked the 10-mile trail. if she hiked a total of 90 miles, which equation can be used to find the number of times maria hiked each trail? x + y = 90 5x – 10y = 90 90 – 10y = 5x 90 + 10y = 5x

c. y = 1/4 x + 5

step-by-step explanation:

first, put the equation of the line on the graph into slope-intercept form

(y = mx + b):   y = -4x + 8

second, a perpendicular line has to have "an opposite/reciprocal slope" to the original slope. so, find the "m" value in your original equation (it's -4, right? )

original slope: m = -4   perpendicular slope: change the sign to its opposite and find the reciprocal ("flip" the number)

new slope is now positive (b/c the original slope was negative 4), and it's 1/4 (not the original slope of 4 or 4/1)