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
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for
and for
but