Question

Determine the point that is 3/4 the distance from the endpoint (−6,−16)(−6,−16) of the segment with endpoints (34,2)(34,2) and (−6,−16)(−6,−16).
what, pls explain cus there is other questions similar to this​

Answer 1

Answer:

The location of the point that is 3/4 the distance from $A(x,y)$ is $C(x,y) = (24, -2.5)$.

Step-by-step explanation:

Let $A(x,y) = (-6,-16)$ and $B(x,y) = (34,2)$ the endpoints of the segment, we can determine the location of the point that is 3/4 the distance from $A(x,y)$ by the following vector equation:

$C(x,y) = A(x,y) + \frac{3}{4}\cdot (B(x,y)-A(x,y))$ (1)

If we know that $A(x,y) = (-6,-16)$ and $B(x,y) = (34,2)$, the location of $C(x,y)$ is:

$C(x,y) = (-6,-16)+\frac{3}{4}\cdot [(34,2)-(-6,-16)]$

$C(x,y) = (-6,-16)+\frac{3}{4}\cdot (40,18)$

$C(x,y) = (24, -2.5)$

The location of the point that is 3/4 the distance from $A(x,y)$ is $C(x,y) = (24, -2.5)$.