Coordinate Geometry

Coordinate Geometry

Let the Straight Lines AB: x + y − 2 = 0 and AC: 3y − x = 2 Intersect the x-axis at B and C Respectively. If P Is the Orthocentre of Triangle ABC, Then the Area of Triangle CPB Is
ByShiwam September 22, 2026September 16, 2026

Lines AB: x+y−2=0 and AC: 3y−x=2 meet the x-axis at B and C. Find the area of triangle CPB, where P is the orthocentre of triangle ABC.

Read More Let the Straight Lines AB: x + y − 2 = 0 and AC: 3y − x = 2 Intersect the x-axis at B and C Respectively. If P Is the Orthocentre of Triangle ABC, Then the Area of Triangle CPB Is
Coordinate Geometry

Distance of Origin From Centroid — Two Sides and Orthocenter Given
ByShiwam September 14, 2026September 10, 2026

Given two sides of a triangle and its orthocenter, find the distance from the origin to the centroid by locating the altitudes and the third vertex.

Read More Distance of Origin From Centroid — Two Sides and Orthocenter Given
Coordinate Geometry

Triangle ABC: y=x Bisects ∠B, AC is 2x−y=2, 2AB=BC, A=(4,6) — Find α+2β
ByShiwam September 8, 2026September 10, 2026

In triangle ABC, y=x bisects angle B, AC is 2x−y=2, and 2AB=BC. Given A=(4,6) and B=(α,β), find α+2β using the angle bisector’s side-ratio property.

Read More Triangle ABC: y=x Bisects ∠B, AC is 2x−y=2, 2AB=BC, A=(4,6) — Find α+2β
Coordinate Geometry

A Line With Slope Greater Than One Passes Through the Point A(4, 3) and Intersects the Line x − y − 2 = 0 at the Point B. If the Length of AB Is √29/3, Then B Also Lies on the Line
ByShiwam September 5, 2026September 16, 2026

A line through A(4,3) with slope greater than 1 meets x−y−2=0 at B, with AB=√29/3. Find which of four given lines B lies on.

Read More A Line With Slope Greater Than One Passes Through the Point A(4, 3) and Intersects the Line x − y − 2 = 0 at the Point B. If the Length of AB Is √29/3, Then B Also Lies on the Line