Question

Let a = (-5, 2) and b = (19, 9). find coordinates for the point p between a and b that is three fifths of the way from a to

b. find coordinates for the point q between a and b that is three fifths of the way from b to
a.

Answer 1

To find the coordinates for the point P that is three fifths of the way from A to B, we can use the formula P = (1-3/5)A + (3/5)B.

Step-by-step explanation:

To find the coordinates for the point P between A and B that is three fifths of the way from A to B, we can use the formula:

P = (1-3/5)A + (3/5)B

Plugging in the values:

P = (1-3/5)(-5,2) + (3/5)(19,9)

Simplifying:

P = (2/5)(-5,2) + (3/5)(19,9)

P = (-2, 4/5) + (11.4, 5.4)

P = (-2+11.4, 4/5+5.4)

P = (9.4, 9.8)

Therefore, the coordinates for the point P are (9.4, 9.8).

To find the coordinates for the point Q between A and B that is three fifths of the way from B to A, we can use the formula:

Q = (1-3/5)B + (3/5)A

Plugging in the values:

Q = (1-3/5)(19,9) + (3/5)(-5,2)

Simplifying:

Q = (2/5)(19,9) + (3/5)(-5,2)

Q = (7.6, 3.6) + (-3, 4/5)

Q = (7.6-3, 3.6+4/5)

Q = (4.6, 8.2)

Therefore, the coordinates for the point Q are (4.6, 8.2).

Answer 2

In this question we need to use ratio formula which is

`( (k_(1) x_(2) +k_(2)x_(1))/(k_(1)+k_(2)) , (k_(1) y_(2) +k_(2)y_(1))/(k_(1)+k_(2)) )`

a .Here

`k_(1):k_(2)= 3/5:2/5=3:2, x_(1) =-5 , x_(2) =19 , y_(1)=2 , y_(2)=9`

So the required point is

`p = ((3*19+2*(-5))/(3+2),(3*9+2*2)/(3+2) )`

`p =((47)/(5),(31)/(5) )`

b.And for point q,

`k_(1):k_(2)= 3:2, x_(1) =19 , x_(2) =-5 , y_(1)=9 , y_(2)=2`

Substituting these values in the formula, we will get

`q =((3*(-5)+2*(19))/(3+2) , (3*2+2*9)/(3+2) )`

`q =((23)/(5),(24)/(5))`