Question 4
The gradient of the line joining the two points and is .
a) Write down the gradient of the line which is parallel to .
b) Write down the gradient of the line which is perpendicular to .
c) Find the equation of the line parallel to and passing through the point .
Give your final answer in standard form .
d) Find the equation of the line perpendicular to and passing through the point
. Give your final answer in standard form .

Ask by Harris Harmon. in Dominica

Mar 31,2025

Question

Question 4
The gradient of the line joining the two points and is .
a) Write down the gradient of the line which is parallel to .
b) Write down the gradient of the line which is perpendicular to .
c) Find the equation of the line parallel to and passing through the point .
Give your final answer in standard form .
d) Find the equation of the line perpendicular to and passing through the point
. Give your final answer in standard form .

Ask by Harris Harmon. in Dominica

Mar 31,2025

UpStudy AI · Accepted Answer

**(a)** The gradient of the line parallel to $$ AB $$ is the same as the gradient of $$ AB $$, so it is  
$$
\frac{3}{4}.
$$

**(b)** The gradient of the line perpendicular to $$ AB $$ is the negative reciprocal of $$\frac{3}{4}$$, so it is  
$$
-\frac{4}{3}.
$$

**(c)** To find the equation of the line parallel to $$ AB $$ that passes through $$(-7,2)$$, we start with the point-slope form:  
$$
y-2=\frac{3}{4}(x+7).
$$  
Multiplying both sides by 4 to eliminate the fraction gives:  
$$
4y-8=3x+21.
$$  
Rearrange the equation into standard form $$ ax+by=c $$:  
$$
3x-4y=-29.
$$

**(d)** To find the equation of the line perpendicular to $$ AB $$ that passes through $$(-4,6)$$, we use the slope $$-\frac{4}{3}$$ in the point-slope form:  
$$
y-6=-\frac{4}{3}(x+4).
$$  
Multiply both sides by 3:  
$$
3y-18=-4x-16.
$$  
Rearrange into standard form:  
$$
4x+3y=2.
$$
**(a)** The gradient of the line parallel to $$ AB $$ is $$ \frac{3}{4} $$. **(b)** The gradient of the line perpendicular to $$ AB $$ is $$ -\frac{4}{3} $$. **(c)** The equation of the line parallel to $$ AB $$ passing through $$(-7,2)$$ is $$ 3x - 4y = -29 $$. **(d)** The equation of the line perpendicular to $$ AB $$ passing through $$(-4,6)$$ is $$ 4x + 3y = 2 $$.

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