Mathematics, 04.10.2020 05:01 masteroftheuniverse3

*. If (2,3) and (-6,5) are the end points of diagonal of a square. Find the equation of another diagonal. Please help with this question..

*. If (2,3) and (-6,5) are the end points of diagonal of a square. Find the equation of another dia

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Answer from: larissacrystalow8g2w

y = 4x + 12 (edited to reflect a SQUARE)

Step-by-step explanation:

Opposite Diagonal of a square means the line goes through the midpoint and has the opposite reciprocal slope.

Use the Midpoint formula: $M=\bigg(\dfrac{x_1+x_2}{2},\dfrac{y_1+y_2}{2}\bigg)$

$M=\bigg(\dfrac{2-6}{2},\dfrac{3+5}{2}\bigg)\\\\\\.\ =\bigg(\dfrac{-4}{2},\dfrac{8}{2}\bigg)\\\\\\.\ =(-2,4)$

Use the Slope formula: $m=\dfrac{y_2-y_1}{x_2-x_1}$

$m=\dfrac{3-5}{2+6}\quad =\quad \dfrac{-2}{8}\quad =\quad -\dfrac{1}{4}$

Opposite Diagonal slope is opposite (change the sign) and reciprocal (flip the fraction) → m⊥ = + 4

Now use the Point-Slope formula: y - y₁ = m⊥(x - x₁) where

(x₁, y₁) is the midpoint (-2, 4)m = 4

y - 4 = 4(x + 2)

y - 4 = 4x + 8

y = 4x + 12

*. If (2,3) and (-6,5) are the end points of diagonal of a square. Find the equation of another diag

Answer from: pravikumar01

Simple question

slope of on le diagonal,whose coordinates are given=

$\frac{y2 - y1}{x2 - x1} = \frac{5 - 3}{ - 6 - 2} = \frac{2}{ - 8} or \: \frac{ - 1}{4}$

now we know that diagonals of square are perpendicular to each other

and we also know that if there are two perpendicular lines have slope m1 and m2 respectively,then

$m1 = \frac{ - 1}{m2}$

so if one diagonal's slope is -1/4 then other diagonal's slope will be 4

now we know that all the equation of a line is in the form

y=mx+c

where m is slope

so simply put the value of m=4

y=4x+c...i)

we also know that the line of equationi) will pass through the midpoint coordinates of first diagonal

mid point of first diagonal ={(2-6)/2 ,(5+3)/2}=(-2,4)

put this value of x and y in i) equation

4=-8+c

c=12

hence putting the value of c in equation I) we get the equation of line as

y=4x+12

y-4x-12=0

Answer from: Quest

step-by-step explanation:

hans did not square the 40-unit side; he merely multiplied it by 2. incorrect.

Hans wanted to find the length of the hypotenuse of the triangle. which statement correctly identifi

Answer from: Quest

answer: c, the green line

step-by-step explanation:

there is no black line, eliminate b.

simple interest implies periodic payments, but the red line shows no payments, eliminate d.

simple interest has equal payments. if paid say every day, the graph is about a straight line (actually a stairstep).

the yellow line is not straight, eliminate a.

check: the green line is straight, answer is c.

simple interest with positive interest rate gives a straight line sloping up to the right. green line:

g(t) = $100 + ($200-$100) ÷ (20 years) × (t years)

= $100 + (4%/year) × ($100)(t years)

incidentally, the yellow line curving upward represents continuously compounded interest

y = $100 × 2^(t years / (14 assuming the yellow line hits $200 at 14 years. 2^0 is 1, so y(0) = $100; 2^(14/14) is 2, so y(14) = $200.

The graph below shows the value of a $100 deposited into three different accounts over a period of 2

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*. If (2,3) and (-6,5) are the end points of diagonal of a square. Find the equation of another diag...