Question

From house to his job as a janitor, you can walk in a straight line. In the afternoon he has to stop twice on his way home. His first stop is at the bodega to get something to eat. The bodega is exactly halfway between his house and the school. The second stop will be at OWL Barbershop for his haircut. The OWL Barbershop location partitions the way from Wilfred’s house and job in the ratio 3:1. The coordinates of his house are H (-3, -4) and his job coordinates are J(5, 0). Please use B to represent the Bodega and O to represent OWL Barbershop.

Answer 1

The coordinates of Bodega is B(1,-2)

The coordinates of OWL Barbershop is O(3,-1)

Explanation:

Coordinates of House H = (-3,-4)

Coordinates of Job J= (5,0)

His first stop is at the bodega to get something to eat. The bodega is exactly halfway between his house and the school.

Let B to represent the Bodega

Now to find coordinates of Bodega we will use use mid point formula since bodega is exactly halfway between his house and the school.

`x=(x_1+x_2)/(2) , y = (y_1+y_2)/(2)\\(x_1,y_1)=(-3,-4)\\(x_2,y_2)=(5,0)\\x=(-3+5)/(2) , y = (-4+0)/(2)\\x=1, y = -2`

So, The coordinates of Bodega is B(1,-2)

Now we are given that The OWL Barbershop location partitions the way from Wilfred’s house and job in the ratio 3:1.

Le O to represent OWL Barbershop.

We will use section formula

`x=(mx_2+nx_1)/(m+n) , y =(my_2+ny_1)/(m+n)\\(x_1,y_1)=(-3,-4)\\(x_2,y_2)=(5,0)\\m:n=3:1\\x=(3(5)+1(-3))/(3+1) , y =(3(0)+1(-4))/(3+1)\\x=3,y=-1`

So, The coordinates of OWL Barbershop is O(3,-1)