Question

Jaydas house is located at (1,5). She can walk in a straight line to get to Christians house. A fast food restaurant is located at (7,2) and partitions the way from jaydas house to cristians house by a ratio of 3:1. Find the coordinates to cristians house
A. (3,4)
B. (5,3)
C. (9,1)
D. (11,0)

Answer 1

Answer:

C. (9,1)

Step-by-step explanation:

Let the coordinated of Jaydas House be:

A(x_1, y_1) = (1,5)

The coordinates of Christian's House be:

B( x_2, y_2)

Let the restaurant be

M(x_M, y_M) = (7,2)

The ratio is 3:1

So

m=3 and n=1

So by the formula of finding the point that divides lines into given ratios

$x_M = \frac{nx_1+mx_2}{m+n}\\7 = \frac{(1)(1)+(3)x_2}{3+1}\\7 = \frac{1+3x_2}{4}\\7*4 = 1 + 3x_2\\28-1=3x_2\\27=3x_2\\x_2 = \frac{27}{3}\\x_2 = 9\\y_M = \frac{ny_1+my_2}{m+n}\\2 = \frac{(1)(5)+(3)y_2}{3+1}\\2 = \frac{5+3y_2}{4}\\2*4 = 5 + 3y_2\\8=5+3y_2\\8-5=3y_2\\3=3y_2\\y_2 = \frac{3}{3}\\y_2 = 1$

Therefore the coordinates of Christian's house are (9,1)

Option C is correct ..