Mathematics, 21.09.2019 22:30 rosetoheart2

Q.2
the x coordinate of a point p is twice its y-coordinate. if p is equidistant
from q (2,-5) and r (-3, 6) find the coordinates of p.
q.3
find the ratio in which y axis divides the line segment joining the points
a (5.-6) and b (-1,-4). also find the coordinates of the point of division.
q.4
find the ratio in which the point(-3, k) divides the line segment joining
the points (-5,-4) and (-2,3). also find the value of k.
find the ratio in which pſ4, m) divides the line segment joining the
q.5
pointsa (2,3) and b(6,-3)hence find m.

Answers: 2

Show answers

Answers

Answer from: nooidbcj

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

Answer from: Quest

step-by-step explanation:

Answer from: Quest

for the friend request.

when a figure, such as triangle (xyz) is reflected over the line y = x to create x'y'z' the x-coordinates and y-coordinates of the original image (pre-image) will be reversed for the image. (e.g., (x, y) > (y, x)) this means that the pre-image position of the x- and y-coordinates switch places which in turn provides a mirror like image of the original xyz.

i notice that when i draw a line segment from x to x', that the points are parallel from each other -- they are exactly across from each other and do not intersect with any other points.

yes, think i would see the same characteristic if you drew the line segment connecting y with the reflecting line and then y' with the reflecting line because of the essence of reflections. because it is a mirror image, each point was effected the same way which leads me to conclude that they same would apply to y and y'.

Another question on Mathematics

Mathematics, 21.06.2019 14:00

Which multiplicative property is being illustrated below? (type commutative, associative, or identity) 5 × 2 × 4 = 2 × 5 × 4

Answers: 1

Answer

Mathematics, 21.06.2019 19:30

Is the figure congruent? yes or no?

Answers: 1

Answer

Mathematics, 21.06.2019 20:00

Need ! the total ticket sales for a high school basketball game were $2,260. the ticket price for students were $2.25 less than the adult ticket price. the number of adult tickets sold was 230, and the number of student tickets sold was 180. what was the price of an adult ticket?

Answers: 1

Answer

Mathematics, 21.06.2019 20:40

Michelle is planting flowers in her garden. she wants the ratio of daises to carnations to be 3 to 2. michelle wants to plant a total of 35 flowers. how many daises should she plant?

Answers: 3

Answer

You know the right answer?

Q.2
the x coordinate of a point p is twice its y-coordinate. if p is equidistant
from q...

Questions