Question

1. given point a(3, -4) and b(8, -6) in the direction ab., what is the coordinate y of the point k that partitions ak of kb in the ratio 3:2. a. -2 b. 0 c. 2 d. 4

Explanation:

Step1: Recall section formula for y-coordinate

For a point dividing segment $AB$ in ratio $m:n$ (from $A$ to $B$), the y-coordinate is $y = \frac{my_B + ny_A}{m+n}$

Step2: Identify values

$m=3$, $n=2$, $y_A=-4$, $y_B=-6$

Step3: Substitute into formula

$y = \frac{3\times(-6) + 2\times(-4)}{3+2}$

Step4: Calculate numerator and denominator

Numerator: $3\times(-6) + 2\times(-4) = -18 -8 = -26$
Denominator: $3+2=5$

Step5: Compute final y-coordinate

$y = \frac{-26}{5} = -5.2$

Note: There is a discrepancy between the calculated result and the provided options. However, following the problem's ratio $AK:KB=3:2$ (point K is outside segment AB beyond B), the calculation is correct. If the ratio was intended to be $KB:AK=3:2$ (K between A and B), the y-coordinate would be $\frac{2\times(-6)+3\times(-4)}{5}=\frac{-12-12}{5}=-4.8$, which also does not match options. If the ratio was $AK:AB=3:2$, the y-coordinate would be $-4 + \frac{3}{2}\times(-2)=-7$, which also does not match.

Answer:

No correct option matches the calculated result. The correct y-coordinate is $\boldsymbol{-5.2}$ or $\boldsymbol{-\frac{26}{5}}$