Question

any one or if you can do both :) .Whoever does this will receive brainliest. ​

Answer 1

By Distance formula, AB =

$ab = \sqrt{ { (x_{2} - x_{1}) }^{2} + ({ y_{2} - y_{1}) }^{2} } \\ = \sqrt{ {(4 - 4)}^{2} + {(5 - ( - 5))}^{2} } \\ = \sqrt{ {0}^{2} + {10}^{2} } \\ = \sqrt{ {10}^{2} } \\ = 10 \\ ab = ap + bp \\ 10 = 4 + bp \\ bp = 10 - 4 \\ bp = 6$

Given that

$\frac{ap}{ab} = \frac{2}{5} \\ 5ap = 2ab \\ 5ap = 2(10) \\ ap = \frac{20}{5} \\ ap = 4$

$\frac{ap}{bp} = \frac{4}{6} = \frac{2}{3}$

By

$p(x.y) = ( \frac{m1x2 + m2x1}{m1 + m2} . \frac{m1y2 + m2y1}{m1 + m2} ) \\ = ( \frac{2(4) + 3(4)}{2 + 3} . \frac{2( - 5) + 3(5)}{2 + 3} ) \\ = ( \frac{8 + 12}{5} . \frac{ - 10 + 15}{5} ) \\ = ( \frac{20}{5} . \frac{5}{5} ) \\ = (4.1)$

Hence the coordinates of point P are (4,1).

Be Brainly!!!;

Answer 2

ab=

(x

2

−x

1

)

2

+(y

2

−y

1

)

2

=

(4−4)

2

+(5−(−5))

2

=

0

2

+10

2

=

10

2

=10

ab=ap+bp

10=4+bp

bp=10−4

bp=6

Given that

\begin{lgathered}\frac{ap}{ab} = \frac{2}{5} \\ 5ap = 2ab \\ 5ap = 2(10) \\ ap = \frac{20}{5} \\ ap = 4\end{lgathered}

ab

ap

=

5

2

5ap=2ab

5ap=2(10)

ap=

5

20

ap=4

\frac{ap}{bp} = \frac{4}{6} = \frac{2}{3}

bp

ap

=

6

4

=

3

2

By

\begin{lgathered}p(x.y) = ( \frac{m1x2 + m2x1}{m1 + m2} . \frac{m1y2 + m2y1}{m1 + m2} ) \\ = ( \frac{2(4) + 3(4)}{2 + 3} . \frac{2( - 5) + 3(5)}{2 + 3} ) \\ = ( \frac{8 + 12}{5} . \frac{ - 10 + 15}{5} ) \\ = ( \frac{20}{5} . \frac{5}{5} ) \\ = (4.1)\end{lgathered}

p(x.y)=(

m1+m2

m1x2+m2x1

.

m1+m2

m1y2+m2y1

)

=(

2+3

2(4)+3(4)

.

2+3

2(−5)+3(5)

)

=(

5

8+12

.

5

−10+15

)

=(

5

20

.

5

5

)

=(4.1)