What is the value of a if the gradient of PR is -2?

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2 Answers
Jan 29, 2018

a=45

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=0y2=1y=2y-intercept

y=0x3=1x=3x-intercept

P=(3,0) and Q=(0,2)

(a)

mQR=12 and R=(2a,y)

using the gradient formula

xm=y2y1x2x1

with Q=(0,2) and R=(2a,y)

y22a0=y22a=12

2(y2)=2a

y2=ay=a+2

R=(2a,a+2)

(b)

using the gradient formula with

P(3,0) and R(2a,a+2)

a+22a3=2

a+2=4a+6

5a=4a=45

Jan 29, 2018

See below.

Explanation:

First the coordinates for P and Q

x=0y2+x3=1y=2P=(xP,yP)=(0,2)
y=0y2+x3=1x=3Q=(xQ,yQ)=(3,0)

Now calling R=(xR,yR)

for [QR]

yRyQxRxQ=12 or

yR02a3=12yR=a32

and for [PR]

yRyPxRxP=2 or

yR22a0=2yR=24a

but

a32=24aa=710