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noname [10]
3 years ago
13

Q.2

Mathematics
1 answer:
Katen [24]3 years ago
5 0

Answer:

Q2. (16,8)

Q3. k=\frac{2}{3}, ratio=5:1

Q4. Ratio=2:1

Q5. Ratio=1:1

Step-by-step explanation:

Q2. Let (2a,a) be the coordinates of P.

Since P is equidistant  from Q (2,-5) and R (-3, 6), we have

|PQ|=|PR|

This gives us:

\sqrt{(2a-2)^2+(a+5)^2}=\sqrt{(2a+3)^2+(6-a)^2}

\implies (2a-2)^2+(a+5)^2=(2a+3)^2+(6-a)^2

Expand:

4a^2-8a+4+a^2+10a+25=4a^2+12a+9+a^2 -12a+36

2a=16

a=8

The coordinates of P are (16,8)

Q.3  The equation of the line segment joining the points

A (5.-6) and B (-1,-4) is x+3y=-13.

The x-coordinate of the point that divides AB in the ratio m:n is

x=\frac{mx_2+nx_1}{m+n}

The y-axis meets this line at (0,-\frac{13}{3})

We substitute x_2=-1,x_1=5,x=0 into this equation and solve for m and n.

0=\frac{-m+5n}{m+n}

m=5n

\frac{m}{n}=\frac{5}{1}

Therefore the ratio is m:n=5:1

Q.4 The equation of the line segment joining

the points (-5,-4) and (-2,3) is -7x+3y=23.

The point (-3, k) must satisfy this line because it lies on it.

-7(-3)+3k=23.

\implies k=\frac{2}{3}

We again use the equation x=\frac{mx_2+nx_1}{m+n} to find the given ratio.

Substitute: x_2=-2,x_1=-5

4=\frac{-2m+-5n}{m+n}

\implies m=2n

\frac{m}{n}= \frac{2}{1}

The ratio is m:n=2:1

Q. 5 The equation of the line joining A (2,3) and B(6,-3) is 3x+2y=12.

We substitute (4,m) to get:

12+4m=12

4m=0

m=0

It is obvious that: (4,0) is the midpoint of A(2,3) and B(6,-3).

Hence the ratio is 1:1

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