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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​

Respuesta :

xero099

Answer:

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

Step-by-step explanation:

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

[tex]C(x,y) = A(x,y) + \frac{3}{4}\cdot (B(x,y)-A(x,y))[/tex] (1)

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

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

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

[tex]C(x,y) = (24, -2.5)[/tex]

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