
In the given figure ABC is a triangle and BC is parallel to the y-axis. AB and AC intersect the y-axis at P and Q respectively.
(i) Write the coordinates of A.
(ii) Find the length of AB and AC.
(iii) Find the ratio in which Q divides AC.
(iv) Find the equation of the line AC.

Answer
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Hint: We can clearly see where the point A is, So note down its coordinates from the diagram. Find the length of AB and AC using distance between two points formula which is mentioned below. The ratio in which Q divides AC can also be calculated using the below mentioned formula. Equation of Ac is found by using two points form a line equation.
1. Distance between two points and is
2. If a point P divides a line in the ratio m:n, then its coordinates will be , where and are the end points on the line.
3. Two points form of a line equation is , where and are the two points.
Complete step-by-step answer:
We are given that ABC is a triangle and BC is parallel to the y-axis.
(i) Coordinates of A is , as the point A is on the x-axis, its y-coordinate will be zero.
So, the correct answer is “ {4,0}”.
(ii) Length of AB and AC
In AB,
Length of AB is units.
In AC,
Length of AC is units.
So, the correct answer is “ units”.
(iii) Ratio in which Q divides AC.
Here Ratio is m:n and
As we can see, Q is on the y-axis, so its x-coordinate will be zero.
Therefore, the coordinates of Q is which are equal to
Corresponding coordinates are equal.
Therefore,
Therefore, Q divides AC in the ratio 2:1.
So, the correct answer is “2:1”.
(iv) Equation of line AC.
Here the two points are
Two points form of a line equation is
This gives,
The equation of line AC is .
So, the correct answer is “ ”.
Note: Distance is a measurement, so it will always have units. If units are not mentioned in the question, you can just put the word “units” after the distance value. When two points are given, we can also find the line equation by finding the slope of the line and then using the slope-point form.
1. Distance between two points
2. If a point P divides a line in the ratio m:n, then its coordinates will be
3. Two points form of a line equation is
Complete step-by-step answer:
We are given that ABC is a triangle and BC is parallel to the y-axis.
(i) Coordinates of A is
So, the correct answer is “ {4,0}”.
(ii) Length of AB and AC
In AB,
Length of AB is
In AC,
Length of AC is
So, the correct answer is “
(iii) Ratio in which Q divides AC.
Here Ratio is m:n and
As we can see, Q is on the y-axis, so its x-coordinate will be zero.
Therefore, the coordinates of Q is
Corresponding coordinates are equal.
Therefore,
Therefore, Q divides AC in the ratio 2:1.
So, the correct answer is “2:1”.
(iv) Equation of line AC.
Here the two points are
Two points form of a line equation is
This gives,
The equation of line AC is
So, the correct answer is “

Note: Distance is a measurement, so it will always have units. If units are not mentioned in the question, you can just put the word “units” after the distance value. When two points are given, we can also find the line equation by finding the slope of the line and then using the slope-point form.
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