Question

Could you please help me and show how you arrived to your answer! I NEED HELPPP

Answer 1

Given:

Coordinate of point A is, A(-3,15).

Coordinate of point B is, B(9,11).

The objective is to find the coordinate of point P which is present at the ratio of 1:1 between A and B.

Consider the given ratio as

$m\colon n=1\colon1$

Consider the coordinate oa point A as,

$(x_1,y_1)=(-3,15)$

Consider the coordinate of point A as,

$(x_2,y_2)=(9,11)$

Then, the coordinate of point P can be calculated as,

$(x,y)=(\frac{m_{}x_2+nx_1}{m+n},\frac{m_{}y_2+ny_1}{m+n})$

Now, substitue all the given values in the above equation.

$\begin{gathered} (x,y)=(\frac{1(9)+1(-3)}{1+1},\frac{1(11)+1(15)}{1+1}) \\ =(\frac{9-3}{2},\frac{11+15}{2}) \\ =(\frac{6}{2},\frac{26}{2}) \\ =(3,13) \end{gathered}$

Hence, the coordinate of the point P is (3,13).