Question

the point Q (3, k) divides the line segment P (9, 4) and R(-9,7) find :
i) the ratio in which point Q divides the join in of point P and R
ii) the value of k
iii) slope of the line parallel to PR

Answer 1

Answer:

Hope it will help you !!!!........

Answer 2

(i)1:2

(ii)k=5

(ii)-$\frac{1}{6}$

Step-by-step explanation:

(i)P(9,4) and R(-9,7)

Q(3,k) divides the line segment P(9,4) and R(-9,7) in the ratio k:1.

Section formula :$x=\frac{m_1x_2+m_2x_1}{m_1+m_2},y=\frac{m_1y_2+m_2y_1}{m_1+m_2}$

Using the formula

$3=\frac{k(-9)+1(9)}{k+1}$

$3(k+1)=-9k+9$

$3k+3=-9k+9$

$3k+9k=9-3=6$

$12k=6$

$k=\frac{6}{12}=\frac{1}{2}$

Hence, the point Q(3,k) divides the line segment in the ratio 1:2

(ii)Substitute the values

$k=\frac{1(7)+2(4)}{1+2}=\frac{7+8}{3}=\frac{15}{3}=5$

(iii) Slope of PR=$m=\frac{y_2-y_1}{x_2-x_1}=\frac{7-4}{-9-9}=\frac{3}{-18}=-\frac{1}{6}$

Slope of line which is parallel to PR=-$\frac{1}{6}$

Because when two lines are parallel then their slopes are equal.

#Learns more:

https://brainly.in/question/2698752:answered by Shivani