Find the point p along the directed line segment from point a(-16,-8) to point b(0,-17) that divides the segment in the ratio 7 to 6

P(-7.38,-12.85)

Steps:

Draw the directed line in a chart, including points A and B.

Look for the x coordinate of P:

the distance |B-A| along the x coord is |0-(-16)|=16

we are looking for a proportion of 7/13 of that:

the x coord of P is 16*7/13 to the right of -16, or -16+8.62= -7.38

Look for  y coordinate of P:

the distance |B-A| along the y coord is |-17-(-8)|=9

we are looking for a proportion of 7/13 of that:

the y coord of P is 9*7/13 down from -8, or -8-4.85= -12.85

so the point P is P(-7.38,12.85)

3. parallelogram

step-by-step explanation:

we turn each of our sides into direction vectors

ab=b-a=(3 - 7, 1 - 0) = (-4, 1)

bc=c-b=(1,6)

cd=d-c=(4,-1)

da=a-d=(-1,-6)

we see how the opposite sides have negated direction vectors; this is characteristic of a parallelogram.   we have congruent sides ab=cd and bc=da with unequal lengths because 1^2+6^2 is different from (-4)^2+1^2.   so it's not a square or a rhombus.  

we check the dot product of direction vectors of adjacent sides.   we have

ab dot bc = -4(1) + 1(6) = 2

that's not zero so the sides are not perpendicular.   we've ruled out rectangle.

the direction vectors indicate two pairs of congruent parallel sides, so we choose parallelogram over trapezoid.

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step-by-step explanation: