Mathematics, 18.11.2019 10:31 Ezekielcassese

Find the distance between (3, 8) and (7, -11). round to the nearest hundredth.

find the coordinates of the midpoint of jk if j (-9, 5) and k(21, -7).

find the coordinates of the midpoint of ab if a(-8, 7) and b(-9, 11).

if the midpoint between (8, y) and (-11, 6) is (-1.5, 5), find the value of y.

find the slope of the line that passes through the points (3, -6) and (6, 12).

find the value of x so that the line passing through (x, 10) and (-4, 8) has a slope of 2/3

find the value of y so that the line passing through (9, 0) and (3, y) has a slope of 1/2

find the slope of the line that passes through the points (8, 7) and (11, 7).

Find the distance between (3, 8) and (7, -11). round to the nearest hundredth. find the

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Answer from: jonathanmalone

The answers are;

The distance between (3,8)

and

is $19.42\text{ (to the nearest hundredth)}$ The midpoint of the line

The midpoint of the line

The value of

The slope of the line that passes through $(3,-6)\text{ and }(6,12)$ is

The value of

is $-\frac{3}{2}$ The slope of the line that passes through $(8,7)\text{ and }(11,7)$ is

In coordinate geometry, given two points (x_1,y_1) and (x_2,y_2) ;

The distance between them is given by $d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$ The midpoint has the coordinates $(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})$ The slope of the line passing through the points is the ratio $\frac{y_2-y_1}{x_2-x_1}$

These formulae will be used to solve the following problems:

1) Given points (3,8) and (7,-11) , the distance between them is

$\sqrt{(7-3)^2+(-11-8)^2}\approx 19.42 \text{ (to the nearest hundredth)}$

2) If $J=(-9,5) \text{ and }K=(21,-7)$ , the midpoint of the line is

$(\frac{-9+21}{2}, \frac{5+(-7)}{2})=(6,-1)$

3) If $A=(-8,7) \text{ and } B=(-9,11)$ , the midpoint of the line is

$(\frac{-8+(-9)}{2}, \frac{7+11}{2})=(8.5,9)$

4) If the midpoint between $(8,y) \text{ and } (-11,6)$ is (-1.5,5) , then, using the

midpoint formula for the y-coordinate

$6=\frac{y+5}{2} \implies y=7$

5) The slope of the line that passes through $(3,-6)\text{ and }(6,12)$ is

$\frac{12-(-6)}{6-3}=6$

6) If the slope of the line that passes through $(x,10)\text{ and }(-4,8)$ is $\frac{2}{3}$ , then,

using the slope formula

$\frac{2}{3}=\frac{8-10}{-4-x}\\\implies \frac{2}{3}=\frac{10-8}{4+x}\\\implies \frac{2}{3}=\frac{2}{4+x}\\\implies x=-1$

7) If the slope of the line that passes through $(9,0)\text{ and }(3,y)$ is $\frac{1}{2}$ , then,

using the slope formula

$\frac{1}{2}=\frac{y-0}{3-9}\\\implies \frac{1}{2}=\frac{y}{-3}\\\implies y=-\frac{3}{2}$

8) The slope of the line that passes through $(8,7)\text{ and }(11,7)$ is

$\frac{7-7}{11-8}=0$ , (since the y-coordinates of both points are equal)

Learn more about gradients here: link

Answer from: breannaasmith1122

Distance formula : d = sqrt (x2 - x1)^2 + (y2 - y1)^2
(3,8)(-7,11)
d = sqrt (-7 - 3)^2 + (11 - 8)^2
d = sqrt (-10^2) + (3^2)
d = sqrt (100 + 9)
d = sqrt 109
d = 10.44

mid-point formula : ((x1 + x2) / 2 , (y1 + y2) / 2)
(-9,5)(21,-7)

midpoint = ((-9 + 21)/2 , (5 + (-7)/2)
= ((12/2) , (-2,2))
= (6, -1) <==

(-8,7)(-9,11)
midpoint = ((-8 + (-9) / 2, (7 + 11)/2 )
= (-17/2, 18/2)
= (-8.5, 9) <==

(8,y)(-11,6)midpoint = (-1.5/5)
midpoint = ((8 + (-11)/2, (y + 6)/2)
= (-3/2), (4 + 6)/2
= (-1.5,5)
y = 4 <==

slope = (y2 - y1) / (x2 - x1)
(3,-6)(6,12)
slope = (12 - (-6) / (6 - 3) = (12 + 6) / 3 = 18/3 = 6 <==

(x,10)(-4,8)...slope = 2/3

y = mx + b
slope(m) = 2/3
(-4,8)...x = -4 and y = 8
sub and find b
8 = 2/3(-4) + b
8 = -8/3 + b
8 + 8/3 = b
24/3 + 8/3 = b
32/3 = b
equation is : y = 2/3x + 32/3 or 3y = 2x + 32
when y = 10
3(10) = 2x + 32
30 - 32 = 2x
-2 = 2x
-2/2 = x
-1 = x <===

(9,0)(3,y)...slope = 1/2

y = mx + b
slope(m) = 1/2
(9,0)...x = 9 and y = 0
sub and find b
0 = 1/2(9) + b
0 = 9/2 + b
-9/2 = b
equation is : y = 1/2x - 9/2 or 2y = x - 9
sub in 3 for x and solve for y
2y = 3 - 9
2y = -6
y = -6/2
y = -3 <==

(8,7)(11,7)...notice how the y values are the same. This means it is a horizontal line. A horizontal line has a slope of 0.

sorry...not too good with the picture graphs

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Find the distance between (3, 8) and (7, -11). round to the nearest hundredth.

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