Respuesta :
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:
[tex]\left(\frac{m_1x_2+m_2x_1}{m_1+m_2},\:\frac{m_1y_2+m_2y_1}{m_1+m_2}\right)[/tex].
Plugging x1,x2, y1, y2, m1 and m2 in above section formula, we get
[tex]\left(\frac{3\cdot 4+7\cdot \left(-2\right)}{3+7},\:\frac{3\cdot 5+7\cdot 1}{3+7}\right)[/tex]
[tex]=\:\left(\frac{12-14}{10},\:\frac{15+7}{10}\right)[/tex]
[tex]=\left(-\frac{2}{10},\frac{22}{10}\right)[/tex]
[tex]\left(-\frac{1}{5},\frac{11}{5}\right)[/tex].
Therefore, y-coordinate of P is [tex]\frac{11}{5}.[/tex]
Correct option is D. 11/5
Answer:
Step-by-step 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:
[tex]P(x,y) = \bigg(\displaystyle\frac{mx_2 + nx_1}{m+n}, \frac{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)[/tex]
Putting all the values:
[tex]P(x,y) = \bigg(\displaystyle\frac{3\times 4 + 7\times -2}{3+7}, \frac{3\times 5 + 7\times 1}{3+7}\bigg)\\\\P(x,y) = (-0.2,2.2)[/tex]
Hence, P(-0.2,2.2) divides the line segment JK in the ratio 3:7.
