Question

Answer this question (◍•ᴗ•◍)❤
Don't give answers if you don't know !!​

Answer 1

Answer:

Given :- a point (6,a) divides the line segment (-3,-1) and(-8,9) in a ratio of k:1

then(6,a)=(k(-8)+1(-3))/k+1,(k(9)+1(-1))/k+1)

6=-8k-3/k+1

k=-9/14

a=9k-1/k+1

=(-19/4(9)-1)/(-9/14+1)

a =-19

Step-by-step explanation:

HOPE YOU understand

THANK YOU

Answer 2

$\large\bf\underline{Question:-}$

A point (6,a) divides the line joining A(-3,-1) and B(-8,9) in the ratio k:1 .find the value of a and k.

━━━━━━━━━━━━━━

$\large\bf\underline{Given:-}$

A point (6,a) divides the line joining A(-3,-1) and B(-8,9) in the ratio of k:1

$\large\bf\underline {To \: find:-}$

Value of a and k.

$\huge\bf\underline{Solution:-}$

Let point P(6,a) divides the joining of the A(-3,-1) and B(-8,9) in tge ratio of k:1.

Section formula:-

$\boxed{ \bf \frac{m_1x_2+m_2x_1}{m_1+m_2},\frac{m_1y_2+m_2y_1}{m_1+m_2} }$

Let m1 = k and m2 = 1

By section formula cordinates of P

$\mapsto \rm \:p(\frac{k\times-8+1\times-3}{k+1},\frac{k\times9+1\times-1}{k+1})$

$\mapsto \rm \:p(\frac{-8k-3}{k+1},\frac{9k-1}{k+1})$

Case (i) :-

• for x cordinate

$\rm \mapsto6 = \frac{ - 8k - 3}{k + 1} \\ \\ \rm \mapsto6(k + 1) = - 8k - 3 \\ \\ \rm \mapsto6k + 6 = - 8k - 3 \\ \\ \rm \mapsto6k + 8k = - 3 - 6 \\ \\ \rm \mapsto14k = - 9 \\ \\ \rm \mapsto \: k = \frac{ - 9}{14}$

Case (ii) :-

for y cordinate

$\mapsto \: \sf a = \dfrac{9 \times \dfrac{-9}{14}-1}{\dfrac{ - 9}{14} +1} \\ \\ \: \mapsto \rm \: a = \dfrac{\dfrac{ - 81 - 14}{14}}{\dfrac{ - 9 + 14}{14}} \\ \\ \rm \mapsto \: a = \dfrac{\dfrac{ - 95}{14}}{\dfrac{ 5}{14}} \\ \\ \rm \mapsto \: a = \frac{ - 95}{14} \times \frac{14}{5} \\ \\ \rm \mapsto \: a = \cancel\frac{ - 95}{5} \\\\\bf \mapsto \:a = -19$

Hence,

Value of a = -19 and k = -9/14