What is the value of a if the gradient of PR is -2?
2 Answers
Explanation:
"find the coordinates of P and Q"find the coordinates of P and Q
• " let x = 0, in equation for y-intercept"∙ let x = 0, in equation for y-intercept
• " let y = 0, in equation for x-intercept"∙ let y = 0, in equation for x-intercept
x=0toy/2=1rArry=2larrcolor(red)"y-intercept"x=0→y2=1⇒y=2←y-intercept
y=0tox/3=1rArrx=3larrcolor(red)"x-intercept"y=0→x3=1⇒x=3←x-intercept
rArrP=(3,0)" and "Q=(0,2)⇒P=(3,0) and Q=(0,2)
(a)(a)
m_(QR)=1/2" and "R=(2a,y)mQR=12 and R=(2a,y)
"using the "color(blue)"gradient formula"using the gradient formula
•color(white)(x)m=(y_2-y_1)/(x_2-x_1)∙xm=y2−y1x2−x1
"with "Q=(0,2)" and "R=(2a,y)with Q=(0,2) and R=(2a,y)
rArr(y-2)/(2a-0)=(y-2)/(2a)=1/2⇒y−22a−0=y−22a=12
rArr2(y-2)=2a⇒2(y−2)=2a
rArry-2=arArry=a+2⇒y−2=a⇒y=a+2
rArrR=(2a,a+2)⇒R=(2a,a+2)
(b)(b)
"using the gradient formula with"using the gradient formula with
P(3,0)" and "R(2a,a+2)P(3,0) and R(2a,a+2)
rArr(a+2)/(2a-3)=-2⇒a+22a−3=−2
rArra+2=-4a+6⇒a+2=−4a+6
rArr5a=4rArra=4/5⇒5a=4⇒a=45
See below.
Explanation:
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