If P= (2, 7) and Q= (2, -3), which could be the coordinates of R if triangle PQR is isosceles?

Help me plz will mark brainliest

Ksju [112]

Step-by-step explanation:

Given,

the bigger triangle (∆GFH), <HGF = 90° and <GFH = 60° and GF = 4

In the 30-60-90 triangle, FH = 4×2 = 8

or you can find it like this,

cos60 = 4/FH

FH = 4/cos60 = 8

Now, I is the midpoint of FH, so, FI = 8/2 = 4

now for ∆FGI,

<GFI = 60°, GF = 4, FI = 4, it's a equilateral triangle, so we can say GI = 4

Now we need to find the height of ∆FGI, for that,

area of ∆FGI = (√3/4)×4² = 4√3 = 6.92820323..

So height (GJ) = 2×area/side = 2×4√3/4 = 2√3 = 3.46410162.. [height of ∆GFI (Because altitude is perpendicular distance from a point) = GJ, given]

now, in ∆GJI, GJ = 2√3, GI = 4 and <GJI = 90° (since itsy altitude, the angle will be a right angle, i.e. 90°)

So, JI = √{4²-(2√3)²} = 2

Area = 2×2√3/2 = 2√3 = 3.46410162.. = 3.46 (rounded to the nearest hundredth)

7 0

2 years ago

What is the probability that a point chosen at random on the grid will lie in the shaded region?

Mashcka [7]

Given:

A grid with a shaded region.

To find:

The probability that a point chosen at random on the grid will lie in the shaded region.

Solution:

We have,

Total number of small boxes = 100

Number of blue boxes (shaded region) = 36

Now,

probability that a point chosen at random on the grid will lie in the shaded region is

$\text{Probability}=\dfrac{\text{Number of blue boxes (shaded region)}}{\text{Total number of small boxes}}$

$\text{Probability}=\dfrac{36}{100}$

To find the probability in percent, multiply it by 100.

$\text{Probability}\%=\dfrac{36}{100}\times 100$

$\text{Probability}\%=36\%$

Therefore, the correct option is A.

8 0

2 years ago

Ion get this bro someone help I got school in a hour

worty [1.4K]

Answer:

of Example 6

5 and 14

Step-by-step explanation:

IN EXAMPLE 6

Opposite angles are equal so you equate the first one like this

3x + 20 = 10x - 15

15 + 20 = 7x

35/7 = x

x = 5

In next question b

It is a straight line thus it's 180°

so 4n + 22 +8n -10 = 180

12n + 12 = 180

12n = 180 - 12

n =168÷ 12

n = 14

6 0

2 years ago

PLEASE HELP ME IM LOST! WILL GIVE BRAINLIEST!!!! ABC has vertices A(0,6) B(4,6) C(1,3). Sketch a graph of ABC and use it to find

Paul [167]

The orthocenter is the point where the three altitudes meet.
sketch the graph and you will see that AB is a horizontal line, the altitude is a vertical line through the point (1,3), so the equation of this altitude is x=1

next, find another altitude. I'll use the altitude of BC.
the slope of BC is (6-3)/(4-1)=1, so the slope of the altitude, which is perpendicular to BC going through the point A (0,6), is -1, the equation of the altitude of BC is y=-x+6
the system of equation : x=1
y=-x+6
has a solution (1, 5)
the solution is where the two lines meet, the meeting point is the orthocenter.

Double check by find the equation for other altitude:
slope of AC: (3-6)/(1-0)=-3
slope of altitude of AC: 1/3
equation of altitude of AC: y=(1/3)x+b
the altitude of AC goes through point B (4,6), so we can find out b by plug x=4, y=6 in the equation: 6=(1/3)*4+b, b=14/3
y=(1/3)x+14/3
Is (1,5) also a solution to this equation? Plug x=1 in the equation, we get y=5, so yes, (1,5) is a point on the third altitude.

7 0

2 years ago

Anybody? help me out, please

frosja888 [35]

Answer:

a

Step by step explanation

7 0

2 years ago