Question

The endpoints of AB are ​A(-8​,-6​) and ​B(​-3,-1​). Point C lies on Ab and is 3/5 of the way from A to B. What are the coordinates of point​ C?

Answer 1

Answer: C(-6.125,-4.125)

Explanation:

`\displaystyle\\A(-8,-6)\ \ \ \ B(-3,-1)\\Let\ (3)/(5)=\lambda \\Hence,\\\boxed {x_C=(x_1+x_2\lambda)/(1+\lambda) }\ \ \ \ \ \ \boxed {y_C=(y_1+y_2\lambda)/(1+\lambda) }\\\\x_1=-8\ \ \ \ x_2=-3\\\lambda=(3)/(5) \\\\\lambda=(0.6*5)/(5)\\\\\lambda=0.6\\\\x_C=(-8+(-3)*0.6)/(1+0.6) \\\\x_C=(-8-1.8)/(1.6) \\\\x_C=(-9.8)/(1.6) \\\\x_C=-(9.8*10)/(1.6*10) \\\\x_C=-(98)/(16) \\\\x_C=-6.125\\\\\\`

`\displaystyle\\y_1=-6\ \ \ \ y_2=-1\ \ \ \ \lambda=0.6\\\\y_C=(-6+(-1)*0.6)/(1+0.6) \\\\y_C=(-6-0.6)/(1.6)\\\\y_C=(-6.6)/(1.6) \\\\y_C=-(6.6*10)/(1.6*10) \\\\y_C=-(66)/(16) \\\\y_C=-4.125`

`Thus,\ C(-6.125,-4.125)`