What is the value of a if the gradient of PR is -2?
2 Answers
Explanation:
"find the coordinates of P and Q"
• " let x = 0, in equation for y-intercept"
• " let y = 0, in equation for x-intercept"
x=0toy/2=1rArry=2larrcolor(red)"y-intercept"
y=0tox/3=1rArrx=3larrcolor(red)"x-intercept"
rArrP=(3,0)" and "Q=(0,2)
(a)
m_(QR)=1/2" and "R=(2a,y)
"using the "color(blue)"gradient formula"
•color(white)(x)m=(y_2-y_1)/(x_2-x_1)
"with "Q=(0,2)" and "R=(2a,y)
rArr(y-2)/(2a-0)=(y-2)/(2a)=1/2
rArr2(y-2)=2a
rArry-2=arArry=a+2
rArrR=(2a,a+2)
(b)
"using the gradient formula with"
P(3,0)" and "R(2a,a+2)
rArr(a+2)/(2a-3)=-2
rArra+2=-4a+6
rArr5a=4rArra=4/5
See below.
Explanation:
First the coordinates for
Now calling
for
and for
but