We are given a line AB with its end coordinates. and Another line segment CD which is perpendicular to AB. We have the coordinates of C , and we are asked to find the x intercept of line CD.

For that we need to find the equation of CD

we have coordinates of C , and hence if we have slope of CD we can find equation of CD

Slope of CD can be determine with the help of slope of AB as CD⊥ AB

So, the slope of CD $mCD = -\frac{1}{mAB}$

Hence we start from determining slope of AB

slope is given as

$m= \frac{y_2-y_1}{x_2-x_1}$

$m= \frac{14-(-3)}{7-(-10)}=\frac{17}{17}=1$

Hence $mAB=1$

There fore $mCD=-1$

(∵ Product of Slopes of two perpendicular lines is always -1)

Now we find the equation of CD with the help of slope -1 and coordinates of C(5,12)

$m=\frac{y-y_1}{x-x_1}$

$-1=\frac{y-12}{x-5}$

$-x+5=y-12$

$y=-x+17$

Hence we have our equation , now in order to find the x intercept we keep y = 0 in it and solve for x

$0=-x+17$

$x=17$

Hence the x intercept is 17

8 0

3 years ago

Perform the operation given that a = {−3, −2, −1, 0, 1, 2, 3}, b = {−4, −2, 0, 2, 4}, and c = {0, 1, 2, 3, 4}. (enter your answe

Ludmilka [50]

A ∩ c={0,1,2,3}

b ∪ (a ∩ c)={-4,-2,0,1,2,3,4}

7 0

3 years ago

Write the direct variation function given that y varies directly with x, and y = 1.5 when x = 5.

Cloud [144]

Answer:

y=0.3x

Step-by-step explanation:

Formula = $K=\frac{y}{x}$

y α x

y = kx

Where k is the constant of proportionality.

When y = 1.5; x = 5;

We substitute these known values in the equation,

y = kx

1.5 = k5

Dividing both sides of the equation by 5 to find the value for k, we have

1.5/5= k0.3/5

Therefore,

K = 0.3

Having found the value of k,

We substitute this value into the relationship

y = kx

Therefore we have,

y = 0.3x.

The direct variation function is therefore,

y = 0.3x.

[RevyBreeze]

4 0

2 years ago