Question

Point J(-2,1) and point K(4,5) form a line segment JK. For the point P that partition ms JK in the ratio 3:7, what is the y-coordinate of P?

A. 3/7

B. 6/5

C. 11/7

D. 11/5

Answer 1

Explanation:

We are given the following information in the question:

P divide the line segment JK in the ration 3:7 where J = (-2,1) and K=(4,5)

We use the section formula to calculate coordinates of P.

Formula:

`P(x,y)  = \bigg(\displaystyle(mx_2 + nx_1)/(m+n), (my_2+ny_1)/(m+n)\bigg)\\\\\text{where m:n is the ration in which P divides the line segment JK}\\\text{J have coordinates }(x_1,y_1)\\\text{K have coordinates }(x_2,y_2)`

Putting all the values:

`P(x,y) = \bigg(\displaystyle(3* 4 + 7* -2)/(3+7), (3* 5 + 7* 1)/(3+7)\bigg)\\\\P(x,y) = (-0.2,2.2)`

Hence, P(-0.2,2.2) divides the line segment JK in the ratio 3:7.

Answer 2

We are given coordinates of point J and point K as J(-2,1) and K(4,5).

P divide the JK in ratio m1:m2 =3:7.

We know section formula:

`\left((m_1x_2+m_2x_1)/(m_1+m_2),\:(m_1y_2+m_2y_1)/(m_1+m_2)\right)`.

Plugging x1,x2, y1, y2, m1 and m2 in above section formula, we get

`\left((3\cdot 4+7\cdot \left(-2\right))/(3+7),\:(3\cdot 5+7\cdot 1)/(3+7)\right)`

`=\:\left((12-14)/(10),\:(15+7)/(10)\right)`

`=\left(-(2)/(10),(22)/(10)\right)`

`\left(-(1)/(5),(11)/(5)\right)`.

Therefore, y-coordinate of P is
`(11)/(5).`

Correct option is D. 11/5