Question

Points A(0,7), B(5,2), and C(3,4) are located at A(0,7), B(5,2), and C(3,4). What is the ratio where point C partitions segment BA?

a) 1:2
b) 3:2
c) 2:1
d) 3:1

Answer 1

To find the ratio where point C partitions segment BA, we can use the distance formula to calculate the distances AB, AC, and CB. Using these distances, we can then find the ratio CB/AB : AC/AB.

Step-by-step explanation:

To find the ratio where point C partitions segment BA, we can use the distance formula. First, we need to calculate the distances AB, AC, and CB. AB = √[(x2-x1)2+(y2-y1)2], AC = √[(x2-x1)2+(y2-y1)2], and CB = √[(x2-x1)2+(y2-y1)2]. Then, we can find the ratio using the equation CB/AB : AC/AB.

For this specific problem, AB = √[(5-0)2+(2-7)2] = √(25+25) = 5√2, AC = √[(3-0)2+(4-7)2] = √13, and CB = √[(5-32+(2-4)2] = √8. Therefore, the ratio CB/AB : AC/AB = √8/5√2 : √13/5√2, which simplifies to 2√2/5 : √13/5. This can be written as 2√2 : √13, so the correct answer is option b) 3:2.