Advertisements
Advertisements
Question
The line y = 3x – 2 bisects the join of (a, 3) and (2, −5), find the value of a.
Solution
The given line bisects the join of A(a, 3) and B(2, −5), so the co-ordinates of the mid-point of AB will satisfy the equation of the line.
The co-ordinates of the mid-point of AB are
`((a + 2)/2, (3 - 5)/2)`
= `((a + 2)/2, (-2)/2)`
= `((a + 2)/2, -1)`
Substituting `x = (a + 2)/2 ` and y = –1 in the given equation, we have:
y = 3x – 2
`-1 = 3 xx (a + 2)/2 - 2`
`3 xx (a + 2)/2 = 1`
`a + 2 = 2/3`
`a = 2/3 - 2`
= `(2 - 6)/3`
= `(-4)/3`
APPEARS IN
RELATED QUESTIONS
If the straight lines 3x – 5y = 7 and 4x + ay + 9 = 0 are perpendicular to one another, find the value of a.
Find the equation of a line whose : y-intercept = −1 and inclination = 45°
The co-ordinates of two points A and B are (–3, 4) and (2, –1). Find:
- the equation of AB;
- the co-ordinates of the point where the line AB intersects the y-axis.
Find the equations of the lines passing through point (–2, 0) and equally inclined to the co-ordinate axes.
The vertices of a triangle ABC are A(0, 5), B(−1, −2) and C(11, 7). Write down the equation of BC. Find:
- the equation of line through A and perpendicular to BC.
- the co-ordinates of the point P, where the perpendicular through A, as obtained in (i), meets BC.
Find if the following points lie on the given line or not:
(-1, 5) on the line 3x = 2y -15
The line y = 6- `(3"x")/2` passes through the point (r,3). Find the value of r.
Find the value of a line parallel to the following line:
`(3"y")/4 + (5"y")/2 = 7`
Find the equation of a line passing through (8,3) and making an angle of 45° with the positive direction of the y-axis.
A line AB meets X-axis at A and Y-axis at B. P(4, –1) divides AB in the ration 1 : 2.
- Find the co-ordinates of A and B.
- Find the equation of the line through P and perpendicular to AB.
