Question

If <1=(7−19)°and <2=(+5)°, find the <2

If m<5 = 42° and m<1 = 117°, find m
If M is the midpoint of XY, find the coordinates of X if M(-3,-1) and Y(-8, 6).

Find the distance between the two points. Round to the nearest thousandth.(-8, -2) and (6, -1)

If DE = 4x –1, EF = 9, and DF = 9x –22, find the value of x.

Answer 1

We know that the section formula states that if a point P(x,y) lies on line segment AB joining the points A(x

1

,y

1

) and B(x

2

,y

2

) and satisfies AP:PB=m:n, then we say that P divides internally AB in the ratio m:n. The coordinates of the point of division has the coordinates

P=(

m+n

mx

2

+nx

1

,

m+n

my

2

+ny

1

)

Let C(1,1) divides the line segment AB joining the points A(−2,7) and B(x

2

,y

2

) in the ratio 3:2, then using section formula we get,

C=(

m+n

mx

2

+nx

1

,

m+n

my

2

+ny

1

)

⇒(1,1)=(

3+2

3x

2

+(2×−2)

,

3+2

3y

2

+(2×7)

)

⇒(1,1)=(

5

3x

2

−4

,

5

3y

2

+14

)

⇒1=

5

3x

2

−4

,1=

5

3y

2

+14

⇒5=3x

2

−4,5=3y

2

+14

⇒3x

2

=5+4,3y

2

=5−14

⇒3x

2

=9,3y

2

=−9

⇒x

2

=

3

9

,y

2

=−

3

9

⇒x

2

=3,y

2

=−3

Hence, the point B(x

2

,y

2

) is B(3,−3).