Question

How are points M(-3, 2), P(3, -2), and Q(-3, -2) related to point M(3, 2)? Point N(-3, 2) and point M(3, 2) differ only in the sign of the ×-coordinate. They are reflections of each other across the y-axis. Point P(3, -2) and point M(3, 2) differ only in the sign of the y-coordinate. They are reflections of each other across the x-axis. Point Q(-3, -2) and point M(3, 2) differ in the signs of the ×-coordinate and y-coordinate. They are reflections of each other across both axes

Answer 1

Given:- A line segment joining the points A(−2,−2) and B(2,−4). P is a point on AB such that AP=

7

3

AB.

Now,

AP=

7

3

AB(Given)

7AP=3(AP+BP)

7AP=3AP+3BP

⇒7AP−3AP=3BP

⇒

BP

AP

=

4

3

Therefore,

Point P divides AB internally in the ratio 3:4.

As we know that if a point (h,k) divides a line joining the point (x

1

,y

1

) and (x

2

,y

2

) in the ration m:n, then coordinates of the point is given as-

(h,k)=(

m+n

mx

2

+nx

1

,

m+n

my

2

+ny

1

)

Therefore,

Coordinates of P=(

3+4

3×(2)+4×(−2)

,

3+4

3×(−4)+4×(−2)

)=(

7

−2

,

7

−20

)

Hence, the coordinates of P are (

7

−2

,

7

−20

).

Step-by-step explanation:

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